On bases of certain Grothendieck groups, II

TL;DR

This paper completes the proof of a new basis for the Grothendieck group of unipotent representations of finite Chevalley groups, specifically addressing the type D case.

Contribution

It provides the missing proof for the previously defined basis in type D, advancing the understanding of Grothendieck groups in representation theory.

Findings

Established the basis for type D in the Grothendieck group of unipotent representations.

Confirmed the validity of the new basis in the context of finite Chevalley groups.

Enhanced the theoretical framework for unipotent representation classification.

Abstract

In previous papers the author introduced a new basis of the Grpthendieck group of unipotent representations of a finite Chevalley group. In type D the definition of this basis was stated without proof. In this paper we provide the missing proof.