Divisibility of Character Values of Representations of Coxeter Groups

Jyotirmoy Ganguly; Rohit Joshi

paper

Divisibility of Character Values of Representations of Coxeter Groups

arXiv:2504.18967

Abstract

Let $d$ be a positive integer. We study the proportion of irreducible characters of infinite families of irreducible Coxeter groups whose values evaluated on a fixed element $g$ are divisible by $d$ . For Coxeter groups of types $A_{n}, B_{n}$ and $D_{n}$ , the proportion tends to $1$ as $n$ approaches infinity. For Dihedral groups, which are Coxeter groups of type $I_{2} (n)$ , we compute the limit of the proportion.