From conjugacy classes in the Weyl group to unipotent classes, III

Abstract

Let G G be an affine algebraic group over an algebraically closed field whose identity component G 0 G^{0} is reductive. Let W W be the Weyl group of G G and let D D be a connected component of G G whose image in G / G 0 G/G^{0} is unipotent. In this paper we define a map from the set of “twisted conjugacy classes” in W W to the set of unipotent G 0 G^{0} -conjugacy classes in D D generalizing an earlier construction which applied when G G is connected.