Strata of a disconnected reductive group

Abstract

Let D be a fixed connected component of a reductive algebraic group over an algebraically closed field. We use a variant of the Springer representation to define and study a partition of D into finitely many Strata, one of which is the open set of regular elements. We show that the Strata of D are indexed by a set defined purely in terms of the Weyl group and its automorphism defined by D.