Coxeter Orbits and Modular Representations
Keyword(s):
AbstractWe 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].
1997 ◽
pp. 195-249
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Keyword(s):
1976 ◽
Vol s3-32
(2)
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pp. 347-384
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2012 ◽
pp. 71-80
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2011 ◽
Vol 174
(3)
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pp. 1643-1684
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2002 ◽
Vol 130
(11)
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pp. 3177-3184
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1981 ◽
Vol 22
(1)
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pp. 89-99
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