Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem
Representation Theory
2012-02-20 v3
Abstract
Let (g,[p]) be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p>0. The scheme of tori of maximal dimension of g gives rise to a finite group S(g) that coincides with the Weyl group of g in case g is a Lie algebra of classical type. In this paper, we compute the group S(g) for Lie algebras of Cartan type and provide applications concerning weight space decompositions, the existence of generic tori and polynomial invariants.
Keywords
Cite
@article{arxiv.1003.4358,
title = {Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem},
author = {Jean-Marie Bois and Rolf Farnsteiner and Bin Shu},
journal= {arXiv preprint arXiv:1003.4358},
year = {2012}
}
Comments
32 pages. Minor updates according to referee comments. Accepted for publication in Forum Math