From conjugacy classes in the Weyl group to semisimple conjugacy classes

Jeffrey Adams; Xuhua He; Sian Nie

paper

From conjugacy classes in the Weyl group to semisimple conjugacy classes

arXiv:1903.04089

Abstract

Suppose $G$ is a connected complex semisimple group and $W$ is its Weyl group. The lifting of an element of $W$ to $G$ is semisimple. This induces a well-defined map from the set of elliptic conjugacy classes of $W$ to the set of semisimple conjugacy classes of $G$ . In this paper, we give a uniform algorithm to compute this map. We also consider the twisted case.

28 pages. Final version. To appear in PAMQ