Coxeter orbits and Brauer trees II

Olivier Dudas (1)

1 MI - Mathematical Institute [Oxford]

The purpose of this paper is to discuss the validity of the assumptions (W) and (S) stated in a previous work, about the torsion in the modular l-adic cohomology of Deligne-Lusztig varieties associated to Coxeter elements. We prove that both (W) and (S) hold except for groups of type E_7 or E_8.

Mots clés: Finite reductive groups; Deligne-Lusztig theory; Brauer trees; Broué's conjecture; Generalized Gelfand-Graev representations

Domaines: Théorie des représentations [math.RT]; Théorie des groupes [math.GR]

Olivier Dudas. Coxeter orbits and Brauer trees II. 2010. ⟨hal-00538580v2⟩