scholarly journals Reducibility modulo $p$ of complex representations of finite groups of Lie type: Asymptotical result and small characteristic cases

2002 ◽  
Vol 130 (11) ◽  
pp. 3177-3184 ◽  
Author(s):  
Pham Huu Tiep ◽  
A. E. Zalesskiĭ
Keyword(s):  
Finite Groups ◽  
Representations Of Finite Groups ◽  
Modulo P ◽  
Groups Of Lie Type

scholarly journals Coxeter Orbits and Modular Representations

2006 ◽  
Vol 183 ◽  
pp. 1-34 ◽  
Author(s):  
Cédric Bonnafé ◽  
Raphaël Rouquier
Keyword(s):  
Finite Groups ◽  
Derived Categories ◽  
Modular Representations ◽  
Coxeter Element ◽  
Representations Of Finite Groups ◽  
Groups Of Lie Type

AbstractWe study the modular representations of finite groups of Lie type arising in the cohomology of certain quotients of Deligne-Lusztig varieties associated with Coxeter elements. These quotients are related to Gelfand-Graev representations and we present a conjecture on the Deligne-Lusztig restriction of Gelfand-Graev representations. We prove the conjecture for restriction to a Coxeter torus. We deduce a proof of Brouée’s conjecture on equivalences of derived categories arising from Deligne-Lusztig varieties, for a split group of type An and a Coxeter element. Our study is based on Lusztig’s work in characteristic 0 [Lu2].

UNIPOTENT ELEMENTS IN REPRESENTATIONS OF FINITE GROUPS OF LIE TYPE

2012 ◽  
Vol 11 (02) ◽  
pp. 1250038 ◽  
Author(s):  
L. DI MARTINO ◽  
A. E. ZALESSKI
Keyword(s):  
Normal Subgroup ◽  
Irreducible Representation ◽  
Simple Group ◽  
Finite Groups ◽  
Closed Field ◽  
Group Of Lie Type ◽  
Algebraically Closed Field ◽  
Central Quotient ◽  
Representations Of Finite Groups ◽  
Groups Of Lie Type

Let G be a finite quasi-simple group of Lie type of defining characteristic r > 2. Let H = 〈h, G〉 be a group with normal subgroup G, where h is a non-central r-element of H. Let ϕ be an irreducible representation of H non-trivial on G over an algebraically closed field of characteristic ℓ ≠ r. We show that ϕ(h) has at least two distinct eigenvalues of multiplicity greater than 1, unless G is a central quotient of one of the following groups: SL(2, r), SL(2, 9) or Sp(4, 3), and H = G⋅Z(H).

scholarly journals The generalized Gelfand–Graev characters of GLn(Fq)

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Scott Andrews ◽  
Nathaniel Thiem
Keyword(s):  
Finite Groups ◽  
Type A ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Representations Of Finite Groups ◽  
International Audience ◽  
Unipotent Representations ◽  
Groups Of Lie Type

International audience Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. We use these alternate constructions to show how to obtain generalized Gelfand–Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand–Graev characters in terms of unipotent representations, thereby recovering the Kostka–Foulkes polynomials as multiplicities.

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