Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem

Details Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem

2010-03-23

arxiv.org/abs/1003.4358v3

Mathematics

Representation Theory

32 pages. Minor updates according to referee comments. Accepted for publication in Forum Math

Scientific paper

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.

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