Distinguished conjugacy classes and elliptic Weyl group elements

TL;DR

This paper establishes a correspondence between distinguished conjugacy classes in reductive groups and elliptic conjugacy classes in Weyl groups, revealing structural insights and a homogeneity property.

Contribution

It introduces a new correspondence linking conjugacy classes in reductive groups with elliptic classes in Weyl groups, and proves a related homogeneity property.

Findings

Established a correspondence between conjugacy classes and elliptic Weyl group elements.

Proved a homogeneity property related to this correspondence.

Enhanced understanding of the structure of reductive groups and Weyl groups.

Abstract

We define and study a correspondence between the set of distinguished G^0-conjugacy classes in a fixed connected component of a reductive group G (with G^0 almost simple) and the set of (twisted) elliptic conjugacy classes in the Weyl group. We also prove a homogeneity property related to this correspondence.