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Pré-Publication, Document De Travail Année : 2005

Coxeter orbits and modular representations

Résumé

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 $0$.
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Dates et versions

hal-00014871 , version 1 (30-11-2005)
hal-00014871 , version 2 (15-03-2006)

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Citer

Cédric Bonnafé, Raphaël Rouquier. Coxeter orbits and modular representations. 2005. ⟨hal-00014871v1⟩
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