Leonardo C. Mihalcea, Hiroshi Naruse, Changjian Su
Proc. Japan Acad. Ser. A Math. Sci. 100 (6), 31-36, (June 2024) DOI: 10.3792/pjaa.100.007
KEYWORDS: hook formula, Coxeter group, Kostant and Kumar's twisted group ring, 20F55, 05E16, 16S35
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.
