Representations of Coxeter groups of Lusztig's a-function value 1

TL;DR

This paper characterizes Coxeter group representations with Lusztig's a-function value 1 and identifies all irreducible such representations for specific simply laced Coxeter groups.

Contribution

It provides a complete characterization and classification of irreducible representations with a-function value 1 in certain Coxeter groups.

Findings

Characterization of Coxeter group representations with a-function value 1

Complete classification of irreducible such representations for certain simply laced Coxeter groups

New insights into the structure of these special representations

Abstract

In this paper, we give a characterization of Coxeter group representations of Lusztig's a-function value 1, then determine all the irreducible such representations for certain simply laced Coxeter groups.