Representations of finite groups (Q1098931)

scientific article; zbMATH DE number 4038067

Language	Label	Description	Also known as
English	Representations of finite groups	scientific article; zbMATH DE number 4038067

Statements

instance of

scholarly article

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title

Representations of finite groups (English)

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Journal of Soviet Mathematics

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publication date

1988

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review text

Translation from Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 23, 119-195 (Russian) (1985; Zbl 0606.20008).

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zbMATH Keywords

representations

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characters

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solvable groups

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M-groups

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modular representations

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blocks

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defect groups

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finite groups of Lie type

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reductive algebraic groups

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Chevalley groups

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describes a project that uses

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CROSSED GROUP RINGS OF FINITE GROUPS AND RINGS OF $ p$-ADIC INTEGERS WITH FINITELY MANY INDECOMPOSABLE INTEGRAL REPRESENTATIONS

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Q3963214

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Q3734644

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REPRESENTATIONS OF DIHEDRAL GROUPS OVER A FIELD OF CHARACTERISTIC 2

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On the problem of computing the subdegrees of transitive permutation groups

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Q3672160

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W-graphs of representations of symmetric groups

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Orthogonal decompositions of simple Lie algebras (type $A^ n$)

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Q4740713

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Q3338409

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Q3894070

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Extreme pairs for finite groups

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Large subgroups of the simple group $F_ 2$

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Character distribution of simply reducible groups

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Q3218304

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Problem of modular representations of symmetric groups

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Q4155059

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Q3905475

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Finite groups

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THE CONSTRUCTION OF A MODEL OF REPRESENTATIONS OF THE GENERAL LINEAR GROUP OVER A FINITE FIELD OF ODD CHARACTERISTIC

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The representations of the Weyl groups of type $B_ n$.

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Simple groups and a Diophantine equation

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Q3912951

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Projective modules for $SL(2,2^n)$

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The Green Correspondence and Brauer's Characterization of Characters

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Local methods in block theory

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Block theory with modules

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Periodicity of Weyl modules for SL(2,q)

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The duality operation in the character ring of a finite Chevalley group

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Duality and character values of finite groups of Lie type

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On Springer's correspondence for simple groups of type En (n = 6, 7, 8)

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Cohomology of line bundles on $G/B$

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The first cohomology group of a line bundle on G/B

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On the structure of Weyl modules

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Vanishing theorems and induced representations

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The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B

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On the structure of the cohomology of line bundles on G/B

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Filtrations of cohomology modules for Chevalley groups

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The Projective Indecomposable Modules of SL(2, p n )

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Q3874405

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Principal indecomposable modules for some three-dimensional special linear groups

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Liftings and the zeta functions of the deligne-lusztig varieties

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Unipotent characters of exceptional groups over finite fields fQWith small q

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Unipotent class functions of split special orthogonal groups over finite fields

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The unipotent class functions on the symplectic groups and the odd orthogonal groups over finite fields

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On induced representations for finite groups

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Groups with an Abelian Sylow Subgroup

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Injective modules for restricted enveloping algebras

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Projective Modules for Finite Chevalley Groups

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Clifford's theorem for algebraic groups and Lie algebras

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On the Field of a 2-Block

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Q3949187

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Schur indexes of sporadic simple groups

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Characters of finite groups with dihedral Sylow 2-subgroups

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On the generic algebra of a unipotent subgroup of a finite chevalley group

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The generic degrees of the irreducible characters of e8

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On the Degrees and Rationality of Certain Characters of Finite Chevalley Groups

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On dimension functions of the generic algebra of type $D_n$

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The Symmetric Square and Generic Algebras of Chevalley Groups

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Semilinear automorphisms and dimension functions for certain characters of finite Chevalley groups

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The loewy structure of the projective indecomposable modules for a8in characteristic 2

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The loewy structure of the projective indecomposable modules for a9in characteristic 2

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The Green ring of a finite group

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Solvable groups and algebraic modules

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Q4196583

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On blocks of finite lattice type

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Indecomposable lattices in blocks with cyclic defect groups

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A Criterion for Finite Module Type

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Group extensions, representations, and the Schur multiplicator

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Some numerical results on the characters of exceptional Weyl groups

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Green functions of finite Chevalley groups of type $E_ n (n=6,7,8)$

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On the modular representation of permutation groups of prime power degree

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On the tensor product of permutation modules

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Degrees of Exceptional Characters of Certain Finite Groups

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A monster Lie algebra?

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Q3919888

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Irreducible representations of finite groups of Lie type through block theory and special conjugacy classes

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From Cartan matrices back to groups

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A lower bound for the number of irreducible characters in a block

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Character theory of finite groups with wreathed Sylow 2-subgroups

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On finite groups with cyclic Sylow subgroups. I

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Blocks of characters and structure of finite groups

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Brauer coefficients of p-subgroups associated with a p-block of a finite group

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A Frobenius theorem for blocks

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Characters and local structure in G-algebras

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Q3905490

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Die Zerlegungsmatrizen der Gruppen $PSL(2,p^f)$

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Über die Zerlegungszahlen der Suzukigruppen Sz(q)

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Über die Zerlegungszahlen der unitären Gruppen $PSU(3,2^{2f})$

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A strengthened theory of vertices and sources

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Scott modules and lower defect groups

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Components of induced modules

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Shorter Notes: Character Tables Determine Abelian Sylow 2-Subgroups

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Q4128999

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On the modular representations of the general linear and symmetric groups

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Modular Representations of Finite Groups of Lie Type

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On homomorphisms between Weyl modules and Specht modules

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Projective characters for finite Chevalley groups

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Q4175743

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On the projective characters in characteristic 2 of the groups $SL_3(2^m)$ and $SU_3(2^m)$

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On the projective characters in characteristic 2 of the groups $Suz(2^m)$ and $Sp_4(2^n)$

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A new approach to permutation group representation

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Q3866284

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On the first Cartan invariants in characteristic 2 of the groups $SL_ 3(2^ m)$ and $SU_ 3(2^ m)$

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Defect groups, trivial intersections and character tables

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Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I

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On groups having the same character tables

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Cohomology, hyperalgebras, and representations

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On the tensor product theorem for algebraic groups

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Q3320288

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Symmetric functions, conjugacy classes and the flag variety

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The Coxeter–Todd lattice, the Mitchell group, and related sphere packings

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On irreducible representations of $p$-soluble groups in characteristic $p$

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Reduction theorems for characters of finite groups of Lie type

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A Note on the Connections between the Generalized Characters of Deligne and Lusztig and the Cuspidal Characters of Reductive Groups over Finite Fields

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Representations of finite groups of Lie type

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Truncation and duality in the character ring of a finite group of Lie type

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Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs

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A New Proof of a Theorem of Solomon-Tits

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Homology representations of finite groups of Lie type

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Spherical buildings and the character of the Steinberg representation

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Block extensions

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Normal subgroups of M-groups need not be M-groups

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Character Values and Clifford Extensions for Finite Groups

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Endo-permutation modules over p-groups. I

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Characters of groups with normal extra-special subgroups

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Monomial characters and normal subgroups

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The Green correspondents of simple group modules

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Extending group modules in a relatively prime case

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Some M-subgroups of M-groups

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Complex conjugation of group representations by inner automorphisms

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Representations of reductive groups over finite fields

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Duality for representations of a reductive group over a finite field

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The submodule structure of tyeyl modules for groups of type a1

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The Brauer complex of a Chevalley group

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The centralizers of semisimple elements of the Chevalley groups $E_ 7$ and $E_ 8$

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Q3860002

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Q3904769

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Q3904770

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Remarques sur la dualité de Curtis

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Vertices of irreducible representations of finite Chevalley groups in the describing characteristic

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On irreducible modules over finite - chevalley groups and parabolic subgroups

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On irreducible modules of twisted groups of Lie type

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Imprimitive, Irreducible Complex Characters of the Alternating Group

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A note on decomposition numbers for reductive algebraic groups

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Dihedral defect groups

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The indecomposable modular representations of certain groups with dihedral Sylow subgroup

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Q5634146

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Irreducible Root Systems and Finite Linear Groups of Degree Two

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Blocks whose defect groups are Klein four groups

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On 2-Blocks with Semidihedral Defect Groups

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Projective modules in blocks with elementary Abelian defect groups

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On the representation theory of the symmetric groups

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Minimal splitting fields for group representations

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On Integral Representations of Finite Groups

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Some Properties of Characters of Finite Groups

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Q3955560

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The computations of some Schur indices

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Possible Brauer trees

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Complex linear groups of relatively small degree

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Complex linear groups of odd degree

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Relative normal complements and extendibility of characters

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Finite complex linear groups of degree less than (2q+1)/3

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The blocks of finite general linear and unitary groups

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Brauer trees in $GL(n,q)$

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Groups which determine the Schur index of a representation

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0 references

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0 references

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A natural representation of the Fischer-Griess Monster with the modular function J as character

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On determinants of Cartan matrices of p-blocks

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An Extension Theorem for Characters

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Characters vanishing on all but two conjugacy classes.

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A characteristic class of characters of finite $\pi$-separable groups

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A characterization of characters which arise from -normalizers.

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Invariants for finite groups

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Representations of the hyperoctahedral groups

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A study of certain modular representations

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Artin exponent for arbitrary characters of cyclic subgroups

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A characterization of generalized permutation characters

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A characterization of generalized m-monomial characters

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A character table bound for the Schur index

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On the k(GV) problem

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Tensor induction of generalized characters and permutation characters

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Defect groups and character heights in blocks of solvable groups. II

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Brauer's Height Conjecture for p-Solvable Groups

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Groups whose characters are rational-valued

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Representations and automorphisms of some wreath products

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Real-valued and 2-rational group characters

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Properties of the characters of groups of odd order with respect to a set of primes

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On the number of characters in a p-block of a p-solvable group

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Character values of groups of odd order and a question of Feit

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On the Schur Indices of Characters of Finite Classical Groups

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Representations over p-adic fields of the finite general linear and unitary groups

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Characters of solvable groups induced by linear characters of Hall subgroups

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Properties of the Characters of the Finite General Linear Group Related to the Transpose-Inverse Involution

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Two multiplicity-free permutation representations of the general linear group $GL(n,q^ 2)$

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Q5676386

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Walking around the Brauer tree

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On a Theorem of H. Sawada

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Multiplicities, Scott Modules and Lower Defect Groups

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The friendly giant

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Subgroups inducing the same permutation representation

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Projective Characters of Finite Groups

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On the cartan invariants of sl2(q)

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A conjecture and a theorem on blocks of modular representation

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Darstellungen von $GL(3,F_ q)$ und Gaußsche Summen

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On character values in finite groups

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Q3207182

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Die adjungierten Darstellungen der Chevalley-Gruppen

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Q3708976

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On Joseph's construction of Weyl group representations

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The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Combinatorial and cohomological treatments centering $GL_ n$.

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A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups

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Some classes of monomial groups

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Q4173550

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Principal series representation of finite groups with split bn pairs∗

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Induced cuspidal representations and generalised Hecke rings

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Duality in the Normalizer of a Parabolic Subgroup of a Finite Coxeter Group

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A comparison theorem and other formulae in the character ring of a finite group of Lie type

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Representations of Generic Algebras and Finite Groups of Lie Type

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Representations of complex imprimitive reflection groups

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Ordinary and modular representations of Chevalley groups

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Deligne-Lusztig characters and principal indecomposable modules

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Ordinary and modular characters of $\mathrm{SL}(3,p)$.

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Projective Modular Representations of Finite Groups

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A Characterization of the Projective Characters of a Finite Group

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Rational projective representations of finite groups

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Rational valued and real valued projective characters of finite groups

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The projective characters of the Mathieu group M12 and of its automorphism group

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The projective characters of the Mathieu group M//(22)

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The modular characters of the Higman-Sims simple group

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Projective character tables for the finite simple groups of order less than one million

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Bemerkungen zur modularen Darstellungstheorie. I: Absolut unzerlegbare Moduln

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Q3659962

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Bemerkungen zur modularen Darstellungstheorie. II: Darstellungen von Normalteilern

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Lifting Brauer characters of $p$-solvable groups

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Q4103728

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Extensions of group representations over arbitrary fields

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Primitive characters, normal subgroups, and M-groups

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Character correspondences in solvable groups

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Abelian normal subgroups of M-groups

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Characters of $\pi$-separable groups

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Characters of subnormal subgroups of M-groups

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Generalizations of Taketa's Theorem on the Solvability of M-Groups

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On the decomposition matrices of the symmetric groups. I

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The decomposition of tensors over fields of prime characteristic

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Unipotent representations of the finite general linear groups

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On the minimal dimensions of irreducible representations of symmetric groups

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Trivial source modules for symmetric groups

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The determinant of the Gram matrix for a Specht module

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Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren

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Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.

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Zur Reduktion modulo p der Charaktere von Deligne und Lusztig

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Zur Reduktion modulo p unipotenter Charaktere endlicher Chevalley- Gruppen

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Filtrierungen Der Darstellungen in Der Hauptserie Endlicher Chevalley-Gruppen

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Periodic modules for the group SL(2,q)

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Variations to a theorem of H. Nagao

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The number of representations of a group induced from the irreducible representations of a normal subgroup.

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On representations of finite groups over skewfields

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On induced representations of groups over division rings

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On extension of characters from normal subgroups

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On the irreducible characters of the finite unitary groups

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Q3964778

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Proof of Springer's hypothesis

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Representations of Coxeter groups and Hecke algebras

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A topological approach to Springer's representations

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Q4088979

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Representations of permutation groups II

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Q3734646

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Decomposition numbers of exceptional Weyl groups. I

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Principal series representations of finite Chevalley groups

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Q3337630

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On the vertices of irreducible modules

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Q3915149

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Automorphisms of certain root lattices

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The principal 2-blocks of finite groups with Abelian Sylow 2-subgroups

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A remark on blocks with dihedral defect groups in solvable groups

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The modular Hecke algebra and Steinberg representation of finite Chevalley groups (with an appendix by Peter Landrock)

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On 2-blocks with wreathed defect groups

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On p-blocks of p-solvable groups

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On blocks with central defect groups

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The principal block of finite groups with dihedral Sylow 2-subgroups

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On the number of irreducible characters in a 2-block

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On Centralizers of p-Elements in Indecomposable Modules

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Blocks of groups with a normal p-subgroup

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Principal 2-Blocks of the Simple Groups of Ree Type

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Q3877845

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Q4163370

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A Steinberg Representation for Gl n (Z/p h Z)

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On a conjecture of Alperin and McKay.

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The Schur Index of the p-Regular Characters of the Borel Subgroup

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The spherical building and regular semisimple elements

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Q3048972

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Permutation modules for rank 3 unitary groups

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In search of nonsolvable groups of central type

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The linear index of a group representation

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The complex irreducible characters of Sp(6, q), q even

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Divisibility of Projective Modules of Finite Chevalley Groups by the Steinberg Module

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On the Green Polynomials of Classical Groups

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Irreducible representations of finite classical groups

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UNIPOTENT REPRESENTATIONS OF A FINITE CHEVALLEY GROUP OF TYPE E8

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Q3874401

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Q3861600

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Hecke algebras and Jantzen's generic decomposition patterns

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On a theorem of Benson and Curtis

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Unipotent characters of the symplectic and odd orthogonal groups over a finite field

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Green polynomials and singularities of unipotent classes

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Unipotent Characters of the Even Orthogonal Groups over a Finite Field

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Q5185104

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Q3322289

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Characters of Reductive Groups over a Finite Field. (AM-107)

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The characters of the finite unitary groups

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A theorem on decomposition numbers

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On the irreducible characters of the symmetric group

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On the characters of the Weyl group of type C

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On the characters of the Weyl group of type D

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Multiplicities of principal series representations of finite groups with split (B,N)-pairs

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Irreducible representations of odd degree

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The non-abelian simple groups g, |g| < 106— character tables

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Über 5-Darstellungen der Lyonsgruppe

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Q3934588

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Non-solvable finite groups with cyclic Sylow p-subgroups have non- principal p-blocks

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Character correspondences in finite general linear, unitary and symmetric groups

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Characters of Elements of Finite Order in Lie Groups

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On Certain Groups associated with the Smallest Fischer Group

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Projective Representations of Reflection Groups

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The Modular Permutation Representations of the Known Doubly Transitive Groups

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REPRESENTATIONS OF An, IN CHARACTERISTIC 2 WITH THE 3-CYCLES FIXED-POINT-FREE

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A note on the number of irreducible characters in a p-block with normal defect group

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On decomposability of some Specht modules for symmetric groups

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Submodule structure of some Specht modules

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The idempotents of the symmetric group and Nakayama's conjecture

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Generosity and Characters of Multiply Transitive Permutation Groups

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On p-nilpotent groups with extremal p-blocks

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Q3671358

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Q4182861

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On the Schur indices of GL(n,q) and SL(2n+1,q)

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Module correspondence in finite groups

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Irreducible characters of $p$-solvable groups

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Lower defect groups

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Q3934589

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On subpairs and modular representation theory

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On the number of characters in blocks of finite general linear, unitary and symmetric groups

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Projective representations of extra-special p-groups

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Irreducible projective representations of finite nilpotent groups over number fields

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Projective representations of finite groups in cyclotomic fields

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Q3907721

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Note on the positive definite integral quadratic lattice

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Characterization of groups by their character tables II

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Q3931603

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Q3218280

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Ordinary character theory in a block with a cyclic defect group

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Vertices of irreducible lattices over p-groups

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Group rings of finite groups over p-adic integers

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The weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights

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Induced characters and symplectic sections

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Schur indices of sympletic groups

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Structure locale et caractères

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Sur un théorème de Green

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Pointed groups and construction of characters

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Q3663510

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Q4172210

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The Artin index of characters of finite faithful metacyclic groups

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Q4149599

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Invariants of integral representations

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Invariant lattices and modular decomposition of irreducible representations

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Unzerlegbare Darstellungen endlich-dimensionaler Algebren

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The number of blocks with a given defect group

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Remarks on coherence and the Reynolds isometry

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Counting modular irreducible characters

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Integral representations. Topics in integral representation theory by I. Reiner. Integral representations and presentations of finite groups by K. W. Roggenkamp

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A rank 3 simple group G of order $2^{14} 3^{3} 5^{3}7.13.29$. II: Characters of G and G*

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Q3853819

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Representations of metabelian groups

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A characterization of the modular representations of finite groups with split $(B,N)$-pairs

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On the Clifford theory of blocks of characters

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Lifting modular representations of p-solvable groups

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The vertices of the simple modules of $M_{12}$ over a field of characteristic 2

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Schur indices of irreducible characters of SL(2,q)

0 references

The rank 3 permutation representations of finite groups of type $G_ 2$

0 references

Notes on the Brauer liftings of finite classical groups

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The characters of Weil representations associated to finite fields

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The characters of the finite conformal sympletctic group, CSp(4,q)

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Two remarks on irreducible characters of finite general linear groups

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On the springer representations of the weyl groups of classical algebraic groups

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On the green polynomials of a chevalley group of type f4

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On the Green polynomials of classical groups

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Irreducible modules and parabolic subgroups

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Spin modules in characteristic 2

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Characteristic polynomials of a permutation representation

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Caractères unipotents de ${}^ 3D_ 4({\mathbb{F}}_ q)$

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A property of special representations of Weyl groups.

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On the Schur index and the structure of finite groups

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Minimal Splitting Fields in Cyclotomic Extensions

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A construction of representations of Weyl groups

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A formula for the characteristic function of the unipotent set of a finite Chevalley group

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CHARACTERS OF GL(n , F q ) AND HOPF ALGEBRAS

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Green polynomials op finite classical groups

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Weil representations of finite classical groups

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Representations of finite Chevalley groups. A survey

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Q3905462

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Characters of Finite Groups: Some Uses and Mathematical Applications

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Representations of a subalgebra of the generic algebra corresponding to the weyl group of typeF4

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The reflection character of the finite symplectic and odd-dimensional orthogonal groups

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Reflection compounds and certain $r$-blocks of finite Chevalley groups.

0 references

A reflection sieve for finite BN-pairs of types $A_n$, $B_n$ and $C_n$.

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Reflection compound representations of groups of type A//n,B//n or $C_ n$.

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Reflection sieve obstructions in finite groups of type $D_ n$.

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Reflection compound representations of groups of type $D_ n$.

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On the blocks of certain subgroups of monomial groups

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Q3927382

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Extensions of group representations from a normal subgroup

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Lifting idempotents and Clifford theory

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Representations of groups of order $ph$ in characteristic $p^r$.

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Finite groups and even lattices

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A conjugacy theorem for $E_8$

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Some indecomposable modules of groups with split (B,N)-pairs

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Modular Representations of Finite Groups with Unsaturated Split (B,N)-Pairs

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Weights and admissible pairs

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Composition Factors of the Principal Indecomposable Modules for the Special Linear Group SL(2, q )

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Filtrations with weyl module quotients of the principal indecomposable modules for the group SL(2,q)

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Induzierte Darstellungen in der Theorie der endlichen, algebraischen Gruppen

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Blocks with a normal defect group

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On the number of irreducible characters in a finite group

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Q3867957

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Q3898648

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Some projective representations of $S_n$

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Relations between blocks of a finite group and its subgroup

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Q3967694

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Q3931602

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A note on Brauer's induction theorem

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A Remark on the degree problem in modular representation theory

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The complex Leech lattice and maximal subgroups of the Suzuki group

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Character correspondences in solvable groups

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Character correspondences induced by subgroups of operator groups

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Defect groups and character heights in blocks of solvable groups

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Character-theoretic transfer

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A generalization of the Littlewood-Richardson rule and the Robinson- Schensted-Knuth correspondence

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Representations of finite classical groups. A Hopf algebra approach

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A new approach to permutation group representations. II

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Identifiers

zbMATH Open document ID

0637.20004

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DOI

10.1007/BF01092892

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:1098931