Representations of finite groups of Lie type

DOI10.1090/S0273-0979-1979-14648-2zbMath0416.20002WikidataQ115283014 ScholiaQ115283014MaRDI QIDQ3205399

Charles W. Curtis

Publication date: 1979

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Weyl groupfinite groups of Lie typeinduced charactersHecke algebrairreducible characterfinite Coxeter groupBorel subgroupsemi-simple Lie algebraparabolic subgroupfinite Chevalley groupsLevi decompositionvirtual charactersgeneric algebraprincipal series charactersMacdonald's conjecturesconnected reductive affine algebraic groupirreducible cuspidal charactersdecomposition of induced charactersgroups with split (B,N)-pair

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05)

Related Items

Representations of finite groups, Centers of Generic Hecke Algebras, Cellular algebras, Some infinite dimensional indecomposable modules of Chevalley groups, Multiplicities of principal series representations of finite groups with split (B,N)-pairs, The Steinberg representation, On the depth \(r\) Bernstein projector, The modular Hecke algebra and Steinberg representation of finite Chevalley groups (with an appendix by Peter Landrock), On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives

Cites Work

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• On \(\varepsilon\)-representations
• Semilinear automorphisms and dimension functions for certain characters of finite Chevalley groups
• Buildings of spherical type and finite BN-pairs
• Groups with a (B,N)-pair of rank 2. I
• Unipotent elements and characters of finite Chevalley groups
• Representations of reductive groups over finite fields
• Flag-transitive subgroups of Chevalley groups
• Coxeter orbits and eigenspaces of Frobenius
• On the finiteness of the number of unipotent classes
• Irreducible representations of finite classical groups
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• Reduction theorems for characters of finite groups of Lie type
• The characters of the finite unitary groups
• Principal series representations of finite Chevalley groups
• A theorem on finite Chevalley groups
• The Steinberg character of a finite group with a \((B,N)\)-pair
• On centralizer rings and characters of representations of finite groups
• On the Steinberg characters of finite Chevalley groups
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• The affine group. I: Bruhat decomposition
• Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs
• On the degrees of Steinberg characters of Chevalley groups
• p-adic curvature and the cohomology of discrete subgroups of p-adic groups
• The classes and representations of the groups of 27 lines and 28 bitangents
• Sur certains groupes simples
• The generic degrees of the irreducible characters of e₈
• UNIPOTENT REPRESENTATIONS OF A FINITE CHEVALLEY GROUP OF TYPE E₈
• The Characters of the Finite General Linear Groups
• Prime Power Representations of Finite Linear Groups II
• Discrete Series of GLn Over a Finite Field. (AM-81)
• Adjoint Groups, Regular Unipotent Elements and Discrete Series Characters
• Representations of a subalgebra of the generic algebra corresponding to the weyl group of typeF₄
• On the Green Polynomials of Classical Groups
• The 2-Transitive Permutation Representations of the Finite Chevalley Groups
• On the generic algebra of a unipotent subgroup of a finite chevalley group
• A Note on the Connections between the Generalized Characters of Deligne and Lusztig and the Cuspidal Characters of Reductive Groups over Finite Fields
• Degrees of Irreducible Characters of (B, N)-Pairs of Types E 6 and E 7
• Green polynomials op finite classical groups
• Centralizers of Semisimple Elements in Finite Groups of Lie Type
• Endomorphisms of linear algebraic groups
• Modular Representations of Split BN Pairs
• On the Steinberg Character of a Finite Simple Group of Lie Type
• The Characters of the Finite Symplectic Group Sp(4,q)
• Eisenstein Series over Finite Fields
• On the Degrees and Rationality of Certain Characters of Finite Chevalley Groups
• Numbers of solutions of equations in finite fields
• A Geometric Approach to the Representations of the Full Linear Group Over a Galois Field