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 a previous paper on regular unipotent elements.
Publié le : 2004-07-05
Classification:
Unipotent elements,
regular elements,
Levi subgroups,
root system,
MSC Primary 20G15; Secondary 20G40,
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
@article{hal-00318678,
author = {Bonnaf\'e, C\'edric},
title = {Sur les \'el\'ements unipotents r\'eguliers des sous-groupes de Levi},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00318678}
}
Bonnafé, Cédric. Sur les éléments unipotents réguliers des sous-groupes de Levi. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00318678/