Parametrizing unipotent representations

TL;DR

This paper unifies the definitions of a new basis for the Grothendieck group of unipotent representations across classical and exceptional types of Chevalley groups over finite fields.

Contribution

It reconciles previously different definitions of a basis for unipotent representations in classical and exceptional types.

Findings

Unified the basis definitions for classical and exceptional types.

Provided a consistent framework for unipotent representation parametrization.

Clarified the structure of the Grothendieck group for these representations.

Abstract

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In this paper we reconcile the two definitions.