Open Access
June 2024 Hook formula for Coxeter groups via the twisted group ring
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

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.

Citation

Download Citation

Leonardo C. Mihalcea. Hiroshi Naruse. Changjian Su. "Hook formula for Coxeter groups via the twisted group ring." Proc. Japan Acad. Ser. A Math. Sci. 100 (6) 31 - 36, June 2024. https://doi.org/10.3792/pjaa.100.007

Information

Published: June 2024
First available in Project Euclid: 2 June 2024

Digital Object Identifier: 10.3792/pjaa.100.007

Subjects:
Primary: 05E16 , 16S35 , 20F55

Keywords: Coxeter group , hook formula , Kostant and Kumar's twisted group ring

Rights: Copyright © 2024 The Japan Academy

Vol.100 • No. 6 • June 2024
Back to Top