Distinguished strata in a reductive group

TL;DR

This paper extends the concept of distinguished unipotent classes to the broader set of strata in a reductive group, introducing and analyzing strata of a Weyl group to deepen understanding of group structure.

Contribution

It introduces the notion of distinguished strata within reductive groups and studies the associated Weyl group strata, expanding the classification framework.

Findings

Extended the notion of distinguished unipotent classes to strata

Introduced and analyzed Weyl group strata

Provided new insights into the structure of reductive groups

Abstract

The set of strata of a reductive group can be viewed as an enlargement of the set of unipotent classes. In this paper the notion of distinguished unipotent class is extended to this larger set. The strata of a Weyl group are introduced and studied.