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2006 Coxeter orbits and modular representations
Cédric Bonnafé, Raphaël Rouquier
Nagoya Math. J. 183: 1-34 (2006).


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].


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Cédric Bonnafé. Raphaël Rouquier. "Coxeter orbits and modular representations." Nagoya Math. J. 183 1 - 34, 2006.


Published: 2006
First available in Project Euclid: 5 September 2006

zbMATH: 1109.20038
MathSciNet: MR2253885

Primary: 20G05
Secondary: 18E30 , 20G40

Rights: Copyright © 2006 Editorial Board, Nagoya Mathematical Journal

Vol.183 • 2006
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