Séminaire Lotharingien de Combinatoire, B93d (2025), 18 pp.

Jyotirmoy Ganguly and Rohit Joshi

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 groups whose values evaluated at 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 I₂(n), we compute the limit of the proportion.

Received: April 29, 2025. Revised: January 15, 2026. Accepted: February 2, 2026.

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