Hook formula for Coxeter groups via the twisted group ring
arXiv:2401.06516 · doi:10.3792/pjaa.100.007
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.
12 pages