Rational Catalan numbers for complex reflection groups ☆

Assuming standard conjectures, we show that the canonical symmetrizing trace on the Hecke algebra of irreducible spetsial complex reflection groups produces rational Catalan numbers when evaluated at powers of a Coxeter element. This extends a technique used by Galashin, Lam, Trinh, and Williams to uniformly prove the enumeration of their noncrossing Catalan objects for finite Coxeter groups. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).