Harish-Chandra Theorem for the Multi-Parameter Quantum Groups of Okado-Yamane Type
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915879174799360 |
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| author | Chen, Kaixiang Hu, Naihong Wang, Hengyi |
| author_facet | Chen, Kaixiang Hu, Naihong Wang, Hengyi |
| contents | This paper is devoted to studying the centre of the multi-parameter quantum group $U_{q,G}(\mathfrak{g})$ introduced by Okado and Yamane, where $\mathfrak{g}$ is a complex simple Lie algebra, and all parameters lie in general position. We mainly establish the Harish-Chandra theorem, proving that the Harish-Chandra homomorphism is an isomorphism; in particular, we determine the centre $Z(U_{q,G})\cong (U^0_\flat)^W$ is isomorphic to a polynomial algebra or a quotient algebra of a polynomial algebra. The same result holds for the $(U^0_\flat)^W$ of the two-parameter quantum group $U_{r,s}(\mathfrak{g})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harish-Chandra Theorem for the Multi-Parameter Quantum Groups of Okado-Yamane Type Chen, Kaixiang Hu, Naihong Wang, Hengyi Quantum Algebra Representation Theory 17B37 (Primary) 17B35, 81R50 (Secondary) This paper is devoted to studying the centre of the multi-parameter quantum group $U_{q,G}(\mathfrak{g})$ introduced by Okado and Yamane, where $\mathfrak{g}$ is a complex simple Lie algebra, and all parameters lie in general position. We mainly establish the Harish-Chandra theorem, proving that the Harish-Chandra homomorphism is an isomorphism; in particular, we determine the centre $Z(U_{q,G})\cong (U^0_\flat)^W$ is isomorphic to a polynomial algebra or a quotient algebra of a polynomial algebra. The same result holds for the $(U^0_\flat)^W$ of the two-parameter quantum group $U_{r,s}(\mathfrak{g})$. |
| title | Harish-Chandra Theorem for the Multi-Parameter Quantum Groups of Okado-Yamane Type |
| topic | Quantum Algebra Representation Theory 17B37 (Primary) 17B35, 81R50 (Secondary) |
| url | https://arxiv.org/abs/2505.18599 |