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arXiv · 2401.06516

Hook formula for Coxeter groups via the twisted group ring

Leonardo C. Mihalcea·Hiroshi Naruse·Changjian Su
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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.

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BibTeXRIS

Leonardo C. Mihalcea, Hiroshi Naruse, Changjian Su. 2024-01-12. Hook formula for Coxeter groups via the twisted group ring. https://doi.org/10.3792/pjaa.100.007

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