Hook formula for Coxeter groups via the twisted group ring
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915209912778752 |
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| author | Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian |
| author_facet | Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hook formula for Coxeter groups via the twisted group ring Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian Representation Theory Combinatorics Group Theory Rings and Algebras 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. |
| title | Hook formula for Coxeter groups via the twisted group ring |
| topic | Representation Theory Combinatorics Group Theory Rings and Algebras 20F55, 05E16, 16S35 |
| url | https://arxiv.org/abs/2401.06516 |