Title: Weyl groups for non-classical restricted Lie algebras and the Chevalley Restriction Theorem
Abstract: Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mi>š¯”¤</m:mi> <m:mo>,</m:mo> <m:mo>[</m:mo> <m:mi>p</m:mi> <m:mo>]</m:mo> <m:mo>)</m:mo> </m:mrow> </m:math> $(\mathfrak {g},[p])$ 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 š¯”¤ gives rise to a finite group S (š¯”¤) that coincides with the Weyl group of š¯”¤ in case š¯”¤ is a Lie algebra of classical type. In this paper, we compute the group S (š¯”¤) for Lie algebras of Cartan type and provide applications concerning weight space decompositions, the existence of generic tori and polynomial invariants.