An extension of a theorem and errata for "A Class of Representations of Hecke Algebras"

TL;DR

This paper extends a key theorem about the acyclicity of certain Coxeter group modules to broader classes of groups and graphs, and provides errata for the original publication.

Contribution

It generalizes a theorem on Coxeter group modules to include groups with finite dihedral parabolic subgroups and arbitrary scalar edge labels in W-graphs.

Findings

Extended theorem to Coxeter groups with finite dihedral parabolic subgroups

Allowed arbitrary scalar edge labels in W-graphs

Listed errata for the original paper

Abstract

By Theorem~1.12 of the paper "A Class of Representations of Hecke Algebras", if $W$ is a Coxeter group whose proper parabolic subgroups are finite, and if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a $W$-graph, then $\Gamma$ must be acyclic. Here we extend this result to Coxeter groups with finite dihedral parabolic subgroups and $W$-graphs with arbitrary scalar edge labels. Also, errata for the paper are listed in the last section.