Abstract
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 $0$ [Lu2].
Citation
Cédric Bonnafé. Raphaël Rouquier. "Coxeter orbits and modular representations." Nagoya Math. J. 183 1 - 34, 2006.
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