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Éléments unipotents réguliers des sous-groupes de Levi

Published online by Cambridge University Press:  20 November 2018

Cédric Bonnafé
Cédric Bonnafé*
Affiliation:
Département de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25000 Besançon, France email: bonnafe@math.univ-fcomte.fr
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Résumé

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Nous étudions la structure du centralisateur d'un élément unipotent régulier d'un sous-groupe de Levi d'un groupe réductif, ainsi que la structure du groupe des composantes de ce centralisateur en relation avec la notion de système local cuspidal définie par Lusztig. Nous déterminons son radical unipotent, montrons l'existence d'un complément de Levi et étudions la structure de son groupe de Weyl. Comme application, nous démontrons des résultats qui étaient annoncés dans un précédent article de l'auteur sur les éléments unipotents réguliers.

Abstract

Abstract

We investigate the structure of the centralizer of a regular unipotent element of a Levi subgroup of a reductive group. We also investigate the structure of the group of components of this centralizer in relation with the notion of cuspidal local system defined by Lusztig. We determine its unipotent radical, we prove that it admits a Levi complement, and we get some properties on its Weyl group. As an application, we prove some results which were announced in previous paper on regular unipotent elements.

Keywords

20G
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 2 , 01 April 2004 , pp. 246 - 276
Copyright
Copyright © Canadian Mathematical Society 2004

References

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