Cohomology of Deligne-Lusztig varieties for groups of type A

Olivier Dudas (1)

1 MI - Mathematical Institute [Oxford]

We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of GLn(q). We show that the geometric version of Broué's conjecture over Q_\ell, together with Craven's formula, holds for any unipotent block whenever it holds for the principal Phi_1-block, that is for the variety X(\pi).

Mots clés: Finite reductive groups; Broué's conjecture; Deligne-Lusztig theory; Representations of the symmetric group

Domaines: Théorie des représentations [math.RT]

Olivier Dudas. Cohomology of Deligne-Lusztig varieties for groups of type A. 2011. ⟨hal-00654560⟩