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Coxeter Orbits and Modular Representations

Published online by Cambridge University Press:  11 January 2016

Cédric Bonnafé  and
Raphaël Rouquier
Cédric Bonnafé
Affiliation:
Céedric Bonnafée Univ. de Franche-Comtée Déepartement de Mathéematiques (CNRS UMR 6623) 16 Route de Gray 25000 Besan¸con France bonnafe@math.univ-fcomte.fr http://www-math.univ-fcomte.fr/pp_Annu/CBONNAFE/
Raphaël Rouquier
Affiliation:
Institut de Mathématiques de Jussieu — CNRS UFR de Mathématiques, Université Denis Diderot 2, place Jussieu, 75005 Paris France and Department of Pure Mathematics University of Leeds Leeds LS2 9JT U.K. rouquier@math.jussieu.fr
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Abstract

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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 Brouée’s conjecture on equivalences of derived categories arising from Deligne-Lusztig varieties, for a split group of type An and a Coxeter element. Our study is based on Lusztig’s work in characteristic 0 [Lu2].

Keywords

20G0518E3020G40

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 183 , 2006 , pp. 1 - 34
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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