Unipotent classes and special Weyl group representations

TL;DR

This paper demonstrates that key invariants of unipotent conjugacy classes in semisimple groups can be derived solely from Weyl group data, linking group invariants to Weyl group representations.

Contribution

It provides a method to recover invariants of unipotent classes using only Weyl group information, establishing a new connection between group theory and Weyl group representations.

Findings

Invariants of unipotent classes are determined by Weyl group data

A new correspondence between unipotent classes and Weyl group representations

Simplifies the study of unipotent classes via Weyl group invariants

Abstract

We show that various invariants of a unipotent conjugacy class in a connected semisimple group can be recovered purely in terms of data involving the Weyl group.