Coxeter Orbits and Modular Representations

By C'edric Bonnaf'e, Raphaël Rouquier. Nagoya mathematical journal, 2005

51 citations recorded by the source corpus.

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 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].

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d7773ca578e78ba9b4fdb4746288e51085dc687

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Derived equivalences and finite dimensional algebras (2006, background): “21 is known to hold when l(wd) = 1 [87] and for GLn and d = n [12].”
Perverse equivalences and Brouéʼs conjecture (2010, background): “That is known in very few cases, and in those cases, defect groups are cyclic [52, 3,18–20].”
Computational proof of the Mackey formula for q>2 (2010, background): “gap> G:=CoxeterGroup("E",6);;PrintDiagram(G); E6 2 | 1 - 3 - 4 - 5 - 6 gap> M:=ReflectionSubgroup(G,[1,3,5,6]); ReflectionSubgroup(CoxeterGroup("E",6), [ 1, 3, 5, 6 ])”