Strata of Weyl groups

TL;DR

This paper investigates the structure of Weyl groups by describing their strata using modified centralizer groups and introduces the concept of superstrata for connected reductive groups, proposing a related conjecture.

Contribution

It provides an explicit description of Weyl group strata via modified centralizer groups and introduces superstrata with a conjecture about their properties.

Findings

Explicit description of Weyl group strata

Introduction of superstrata concept

Proposed conjecture on superstrata

Abstract

A Weyl group W is a union of strata (certain subsets which are unions of conjugacy classes) which are the nonempty fibres of a map from W to the set of irreducible representations of W. We give an explicit description of strata in terms of a certain modified centralizer group. We also define superstrata of a connected reductive group and state a conjecture about them.