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Comptes Rendus Mathématique
Volume 343, n° 1
pages 37-39 (juillet 2006)
Doi : 10.1016/j.crma.2006.04.014
Received : 23 February 2006 ;  accepted : 18 April 2006
On the irreducibility of Deligne-Lusztig varieties
Sur lʼirréductibilité des variétés de Deligne-Lusztig
 

Cédric Bonnafé a , Raphaël Rouquier b, 1
a Laboratoire de mathématiques de Besançon (CNRS-UMR 6623), université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, France 
b Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK 

Abstract

Let G be a connected reductive algebraic group defined over an algebraic closure of a finite field and let   be an endomorphism such that   is a Frobenius endomorphism for some  . Let P be a parabolic subgroup of G. We prove that the Deligne-Lusztig variety   is irreducible if and only if P is not contained in a proper F -stable parabolic subgroup of G. To cite this article: C. Bonnafé, R. Rouquier, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Soit G un groupe réductif connexe défini sur une clôture algébrique dʼun corps fini et soit   un endomorphisme dont une puissance est un endomorphisme de Frobenius. Soit P un sous-groupe parabolique de G. Nous montrons que la variété de Deligne-Lusztig   est irréductible si et seulement si P nʼest pas contenu dans un sous-groupe parabolique F -stable propre de G. Pour citer cet article : C. Bonnafé, R. Rouquier, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
1  Previous address: Équipe des groupes finis (CNRS-UMR 7586), université Paris 7, UFR de mathématiques, 175, rue du Chevaleret, 75013 Paris, France.


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