Endomorphisms of Deligne-Lusztig varieties

François Digne (1) , Jean Michel (1, 2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 IMJ - Institut de Mathématiques de Jussieu

This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general conjectures, in particular that the endomorphism algebra induced on the cohomology is a cyclotomic Hecke algebra, and prove them in some cases. On the way we also prove results on centralizers in braid groups.

Mots clés: braids; cyclotomic Hecke algebras; Deligne-Lusztig varieties

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

François Digne, Jean Michel. Endomorphisms of Deligne-Lusztig varieties. Nagoya Mathematical Journal, 2006, 183, pp.35-63. ⟨hal-00008311⟩