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.

scholarly journals Modular Representations of Finite Groups with Unsaturated Split (B,N)-Pairs

1980 ◽  
Vol 32 (3) ◽  
pp. 714-733 ◽  
Author(s):  
N. B. Tinberg
Keyword(s):  
Finite Group ◽  
Weyl Group ◽  
Prime Number ◽  
Semidirect Product ◽  
Finite Groups ◽  
Modular Representations ◽  
Characteristic P ◽  
Representations Of Finite Groups ◽  
A Finite Group

1. Introduction.Let p be a prime number. A finite group G = (G, B, N, R, U) is called a split(B, N)-pair of characteristic p and rank n if(i) G has a (B, N)-pair (see [3, Definition 2.1, p. B-8]) where H= B ⋂ N and the Weyl group W= N/H is generated by the set R= ﹛ω 1,… , ω n) of “special generators.”(ii) H= ⋂n∈N n-1Bn(iii) There exists a p-subgroup U of G such that B = UH is a semidirect product, and H is abelian with order prime to p.A (B, N)-pair satisfying (ii) is called a saturated (B, N)-pair. We call a finite group G which satisfies (i) and (iii) an unsaturated split (B, N)- pair. (Unsaturated means “not necessarily saturated”.)

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].

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