Coxeter orbits and modular representations

Cédric Bonnafé (1) , Raphaël Rouquier (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IMJ - Institut de Mathématiques de Jussieu

We 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 Broué's conjecture on equivalences of derived categories arising from Deligne-Lusztig varieties, for a split group of type $A_n$ and a Coxeter element. Our study is based on Lusztig's work in characteristic $0$.

Mots clés: finite groups of Lie type; modular representations; Gelfand-Graev; Coxeter orbits

Domaines: Théorie des représentations [math.RT]

Cédric Bonnafé, Raphaël Rouquier. Coxeter orbits and modular representations. Nagoya Mathematical Journal, 2006, 183, pp.1-34. ⟨hal-00014871v2⟩