Some infinite-dimensional representations of certain Coxeter groups

TL;DR

This paper constructs specific infinite-dimensional irreducible complex representations for certain Coxeter groups, utilizing topological features of their Coxeter graphs, expanding understanding of their representation theory.

Contribution

It introduces a new construction method for infinite-dimensional representations of certain Coxeter groups based on topological properties of their graphs.

Findings

Infinite-dimensional irreducible representations exist for non-finite, non-affine Coxeter groups.

Topological features of Coxeter graphs can be used to construct these representations.

The method provides explicit examples of such representations.

Abstract

A Coxeter group admits infinite-dimensional irreducible complex representations if and only if it is not finite or affine. In this paper, we provide a construction of some of those representations for certain Coxeter groups using some topological information of the corresponding Coxeter graphs.