English

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

R2 v1 2026-06-28T14:15:09.807Z