Rationality properties of unipotent representations.

DOI10.1016/S0021-8693(02)00514-8zbMath1141.20300arXivmath/0103232OpenAlexW1991576070MaRDI QIDQ1858266

George Lusztig

Publication date: 12 February 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103232

zbMATH Keywords

Weyl groupsirreducible charactersfinite groups of Lie typeFrobenius mapsHasse principleunipotent representationsDeligne-Lusztig generalized characterssimple algebraic groups of adjoint type

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Representations of finite groups of Lie type (20C33)

Related Items (22)

Galois-equivariant McKay bijections for primes dividing \(q - 1\) ⋮ Unnamed Item ⋮ On the number of irreducible real-valued characters of a finite group ⋮ Galois group action and Jordan decomposition of characters of finite reductive groups with connected center ⋮ Minimal length elements of finite Coxeter groups. ⋮ How to compute the Frobenius-Schur indicator of a unipotent character of a finite Coxeter system. ⋮ Trivial intersection of blocks and nilpotent subgroups ⋮ On the inductive McKay-Navarro condition for finite groups of Lie type in their defining characteristic ⋮ Principal blocks for different primes. I ⋮ Unipotent character sheaves and strata of a reductive group ⋮ The continuity of 𝑝-rationality and a lower bound for 𝑝’-degree characters of finite groups ⋮ Minimal length elements of Coxeter groups. ⋮ Categorical actions on unipotent representations of finite classical groups ⋮ \(\mathrm{Sp}_{2n}(\mathbb F_{q^2})\)-invariants in irreducible unipotent representations of \(\mathrm{Sp}_{4n}(\mathbb F_q)\). ⋮ Brauer trees of unipotent blocks ⋮ Duality, central characters, and real-valued characters of finite groups of Lie type. ⋮ A first guide to the character theory of finite groups of Lie type ⋮ Character degrees in blocks and defect groups ⋮ Frobenius–Schur indicators of unipotent characters and the twisted involution module ⋮ On the Kazhdan–Lusztig cells in type $E_8$ ⋮ Characters and generation of Sylow 2-subgroups ⋮ Multiplicative rule in the Grothendieck cohomology of a flag variety

Cites Work

• Character sheaves. I
• Character sheaves. V
• Representations of reductive groups over finite fields
• Coxeter orbits and eigenspaces of Frobenius
• Minimal length elements in twisted conjugacy classes of finite Coxeter groups.
• The Schur indices of the cuspidal unipotent characters of the finite unitary groups
• Characters of Reductive Groups over a Finite Field. (AM-107)
• Unnamed Item
• Unnamed Item
• Unnamed Item

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