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Coxeter orbits and modular representations

Cédric Bonnafé·Raphaël Rouquier
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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.

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Cédric Bonnafé, Raphaël Rouquier. 2006-03-15. Coxeter orbits and modular representations. https://arxiv.org/abs/math/0511737

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