Modular Representations of Finite Groups of Lie Type

2005 ◽  
Author(s):  
James E. Humphreys
Keyword(s):  
Finite Groups ◽  
Modular Representations ◽  
Representations Of Finite Groups ◽  
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].

scholarly journals Stratifying modular representations of finite groups

2011 ◽  
Vol 174 (3) ◽  
pp. 1643-1684 ◽  
Author(s):  
David Benson ◽  
Srikanth Iyengar ◽  
Henning Krause
Keyword(s):  
Finite Groups ◽  
Modular Representations ◽  
Representations Of Finite Groups

scholarly journals Projective modular representations of finite groups II

1981 ◽  
Vol 22 (1) ◽  
pp. 89-99 ◽  
Author(s):  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Theoretical Background ◽  
Alternating Group ◽  
Modular Representations ◽  
Future Paper ◽  
Representations Of Finite Groups ◽  
Group A ◽  
Mathieu Groups

In this paper, which is a continuation of [4], the necessary theoretical background is given to enable the calculation of the irreducible Brauer projective characters of a given finite group to be carried out. As an example, this calculation is done for the alternating group A (7) in §3. In a future paper the calculations for the Mathieu groups will be presented.

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