Coxeter orbits and modular representations

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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.
24 pages

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Representation Theory, 20C33, 20C20

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http://salesiana.dossiersoluciones.com/handle/123456789/164229

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511737
 http://arxiv.org/abs/math/0511737
 Nagoya Mathematical Journal 183 (2006) 1-34

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arXiv