Cohomology of Deligne-Lusztig varieties for short-length regular elements in exceptional groups

Olivier Dudas (1)

1 MI - Mathematical Institute [Oxford]

We determine the cohomology of Deligne-Lusztig varieties associated to some short-length regular elements for split groups of type F4 and En. As a byproduct, we obtain conjectural Brauer trees for the principal Phi_{14}-block of E7 and the principal Phi_{24}-block of E8.

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

Domaines: Théorie des représentations [math.RT]

Olivier Dudas. Cohomology of Deligne-Lusztig varieties for short-length regular elements in exceptional groups. 2011. ⟨hal-00654558⟩