Cross characteristic representations of symplectic and unitary groups
From MaRDI portal
Publication:1858255
DOI10.1016/S0021-8693(02)00527-6zbMath1025.20002MaRDI QIDQ1858255
Jan Saxl, Pham Hũ'u Tiêp, Kay Magaard, Robert M. Guralnick
Publication date: 12 February 2003
Published in: Journal of Algebra (Search for Journal in Brave)
Weil representationsfinite symplectic groupsminimal polynomialscross characteristic representationsfinite unitary groupsquadratic moduleslow-dimensional representations
Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Representations of sporadic groups (20C34) Representations of finite groups of Lie type (20C33)
Related Items
Quadratic pairs., Commutative Nilpotent Closed Algebras and Weil Representations, Unnamed Item, On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups., Cross characteristic representations of even characteristic symplectic groups, Finite groups admitting Grassmannian 4-designs, On irreducible products of characters, Groups with a \(p\)-element acting with a single non-trivial Jordan block on a simple module in characteristic \(p\), Reduced fusion systems over \(p\)-groups with abelian subgroup of index \(p\). II, On extended Weil representation for finite general linear group and Howe correspondence, Growth of cross-characteristic representations of finite quasisimple groups of Lie type., Moments of Weil representations of finite special unitary groups, Character levels and character bounds for finite classical groups, A problem of Kollár and Larsen on finite linear groups and crepant resolutions, Rational Brauer characters., On prime power order elements of general linear groups., The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups., The structure of rank 3 permutation modules for \(O^\pm_{2n}(2)\) and \(U_m(2)\) acting on nonsingular points., Weil representations of unitary groups over ramified extensions of finite local rings with odd nilpotency length, Eigenvalues of unipotent elements in cross-characteristic representations of finite classical groups., On spectra of covers of finite simple classical groups., The character table of a split extension of the Heisenberg group \(H_1(q)\) by \(\text{Sp}(2,q)\), \(q\) odd., Representation of finite groups: conjectures, reductions, and applications., Monodromy groups of Kloosterman and hypergeometric sheaves, Lusztig induction, unipotent supports, and character bounds, On a conjecture of G. E. Wall., Rank 3 permutation characters and maximal subgroups, Low-Dimensional Complex Characters of the Symplectic and Orthogonal Groups, Extremely primitive groups., Low-dimensional representations of finite orthogonal groups, Generation of finite simple groups by an involution and an element of prime order, Adequate subgroups and indecomposable modules, Localization and finite simple groups., Unitary \(t\)-groups, Minimum polynomials and lower bounds for eigenvalue multiplicities of prime-power order elements in representations of classical groups, Linear groups over \(\text{GF}(2^k)\) generated by a conjugacy class of a fixed point free element of order 3, Symmetric powers and a problem of Kollár and Larsen., CHARACTER LEVELS AND CHARACTER BOUNDS, Regular orbits of quasisimple linear groups. I, Almost cyclic elements in cross-characteristic representations of finite groups of Lie type, MINIMAL IRREDUCIBILITY AND THE UNIPOTENT CHARACTERS OF GROUPS OF TYPE Bm AND Cm, Weil Representations and Some Nonreductive Dual Pairs in Symplectic and Unitary Groups, Absolute Fourth Moments and Finiteness of Linear Groups, On eigenvalues of group elements in representations of simple algebraic groups and finite Chevalley groups., Some aspects of finite linear groups: A survey, Rank 3 permutation modules of the finite classical groups., The non-coprime \(k(GV)\) problem.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The 2-decomposition numbers of Sp(4,q), q odd
- Decomposition numbers of Sp(4,q) for primes dividing \(q\pm 1\)
- Permutation representations and a fragment of the decomposition matrix of symplectic and special linear groups over a finite field
- A characterization of the spinmodule for \(2\cdot A_ n\)
- On the minimal degrees of projective representations of the finite Chevalley groups
- Die Zerlegungsmatrizen der Gruppen \(PSL(2,p^f)\)
- Chevalley groups of odd characteristic as quadratic pairs
- Weil representations associated to finite fields
- On the quadratic pairs
- Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii
- Some generalizations of the Weil representations of the symplectic and unitary groups
- The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups.
- Cross characteristic projective representations for some classical groups
- On the minimal degrees of projective representations of the finite Chevalley groups. II
- Small representations are completely reducible
- Even unimodular lattices associated with the Weil representation of the finite symplectic group
- The blocks of finite general linear and unitary groups
- Lower bounds for degrees of irreducible Brauer characters of finite general linear groups
- Permutation modules for rank 3 symplectic and orthogonal groups
- Sur certains groupes d'opérateurs unitaires
- Representations of symplectic groups
- SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE
- Weil Representations as Globally Irreducible Representations
- Irreducible brauer characters of the 3-dimensional special unitary groups in non-defining characteristic∗
- Quadratic modules for CHEVALLEY groups over fields of odd characteristics
- Regular and Semisimple Blocks of Finite Reductive Groups
- Finite Covers, Cohomology and Homogeneous Structures
- Group Representations and Lattices
- Brauer trees of Sp(4,q)
- Some Representations of Classical Groups
- Quadratic action and the 𝒫(G, V)-theorem in arbitrary characteristic
- Lower bounds for the minima of certain symplectic and unitary group lattices
- Subgroups of Algebraic Groups Containing Regular Unipotent Elements
- Characters of Solvable and Symplectic Groups
- Linear Groups with Orders Having Certain Large Prime Divisors
- Cross characteristic representations of even characteristic symplectic groups
- Minimal characters of the finite classical groups
- Minimal Polynomials and Eigenvalues of p -Elements in Representations of Quasi-Simple Groups with a Cyclic Sylow p -Subgroup
- On the Character of Weil's Representation
- Low-dimensional representations of special unitary groups
- Minimum polynomials and lower bounds for eigenvalue multiplicities of prime-power order elements in representations of classical groups
- Linear groups over \(\text{GF}(2^k)\) generated by a conjugacy class of a fixed point free element of order 3