Rational Catalan Numbers for Complex Reflection Groups
Representation Theory
2023-10-20 v1 Combinatorics
Abstract
Assuming standard conjectures, we show that the canonical symmetrizing trace evaluated at powers of a Coxeter element produces rational Catalan numbers for irreducible spetsial complex reflection groups. 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.
Cite
@article{arxiv.2310.12354,
title = {Rational Catalan Numbers for Complex Reflection Groups},
author = {Weston Miller},
journal= {arXiv preprint arXiv:2310.12354},
year = {2023}
}
Comments
28 pages, 2 figures