Strata and almost special representations

TL;DR

This paper establishes a connection between strata of reductive groups and almost special representations of Weyl groups, providing a new perspective on their structure and classification.

Contribution

It introduces a method to associate finite groups to strata of reductive groups and links these to almost special Weyl group representations in the simply laced case.

Findings

Finite groups are attached to each stratum of a reductive group.

In the simply laced case, strata correspond bijectively to a subset of almost special Weyl group representations.

The results clarify the structure of strata and their representation-theoretic significance.

Abstract

We show how to attach to any stratum of a reductive group a (small) finite group. We also show that in the simply laced case the set of strata is in bijection with a subset of the set of almost special representations of the Weyl group. (This is the same as version 1 except that the abstract has been corrected.)