Divisibility of Character Values of Representations of Coxeter Groups

Abstract

Let d be a positive integer. We study the proportion of irreducible characters of infinite families of irreducible Coxeter roups whose values evaluated at a fixed element g are divisible by d. For Coxeter groups of types An, Bn and Dn, the proportion tends to 1 as n approaches infinity. For dihedral groups, which are Coxeter groups of type I2(n), we compute the limit of the proportion.