Quotient of Deligne-Lusztig varieties

Olivier Dudas (1)

1 MI - Mathematical Institute [Oxford]

We study the quotient of parabolic Deligne-Lusztig varieties by a finite unipotent group U^F where U is the unipotent radical of a rational parabolic subgroup P = L U. We show that in some particular cases the cohomology of this quotient can be expressed in terms of "smaller" parabolic Deligne-Lusztig varieties associated to the Levi subgroup L.

Mots clés: Deligne-Lusztig variety; Deodhar decomposition

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Olivier Dudas. Quotient of Deligne-Lusztig varieties. 2011. ⟨hal-00654092⟩