Hook formula for Coxeter groups via the twisted group ring
Representation Theory
2025-03-25 v1 Combinatorics
Group Theory
Rings and Algebras
Abstract
We use Kostant and Kumar's twisted group ring and its dual to formulate and prove a generalization of Nakada's colored hook formula for any Coxeter groups. For dominant minuscule elements of the Weyl group of a Kac--Moody algebra, this provides another short proof of Nakada's colored hook formula.
Keywords
Cite
@article{arxiv.2401.06516,
title = {Hook formula for Coxeter groups via the twisted group ring},
author = {Leonardo C. Mihalcea and Hiroshi Naruse and Changjian Su},
journal= {arXiv preprint arXiv:2401.06516},
year = {2025}
}
Comments
12 pages