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

DOI10.1090/S0273-0979-1979-14690-1zbMath0485.20029MaRDI QIDQ3944765

Dean Alvis

Publication date: 1979

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

zbMATH Keywords

Frobenius mapChevalley groupreductive algebraic groupcharacter ringSteinberg charactervirtual charactersduality operatorcuspidal characters

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05) Integral representations of finite groups (20C10) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Character sheaves. III, Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field. I, Representations of Generic Algebras and Finite Groups of Lie Type, Sheaves on buildings and modular representations of Chevalley groups, On an invariant bilinear form on the space of automorphic forms via asymptotics, L’involution de Zelevinski modulo ℓ, Representations of finite groups, Duality for classical 𝑝-adic groups: The half-integral case, On the Gan-Gross-Prasad problem for finite unitary groups, Deligne-Lusztig duality and wonderful compactification, On the \(E\)-polynomials of a family of \({\mathrm {Sl}}_n\)-character varieties, Deligne–Lusztig duality on the moduli stack of bundles, Alvis-Curtis duality for representations of reductive groups with Frobenius maps, Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents, Alvis-Curtis duality for finite general linear groups and a generalized Mullineux involution, p-adic analog of the Kazhdan-Lusztig hypothesis, Unipotent characters of the symplectic and odd orthogonal groups over a finite field, Duality for representations of a reductive group over a finite field, Duality and character values of finite groups of Lie type, Multiplicities of principal series representations of finite groups with split (B,N)-pairs, Generalized Blocks of Unipotent Characters in the Finite General Linear Group, Duality for Representations of a Hecke Algebra, Duality, central characters, and real-valued characters of finite groups of Lie type., Character sheaves on disconnected groups, VIII, Principal series components of the gelfand characters of a finite group with a split (bn)-pair of characteristic p, Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz., The explicit Zelevinsky–Aubert duality

Cites Work

• Unnamed Item
• A formula for the characteristic function of the unipotent set of a finite Chevalley group
• Truncation and duality in the character ring of a finite group of Lie type
• Representations of reductive groups over finite fields
• Reduction theorems for characters of finite groups of Lie type
• The Steinberg character of a finite group with a \((B,N)\)-pair