Braid group action and quantum affine superalgebra for type $\mathfrak{osp}(2m+1|2n)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913905943511040 |
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| author | Wu, Xianghua Lin, Hongda Zhang, Honglian |
| author_facet | Wu, Xianghua Lin, Hongda Zhang, Honglian |
| contents | In this paper, we investigate the structure of the quantum affine superalgebra associated with the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m\geqslant 1$. The Drinfeld-Jimbo presentation for this algebra, denoted as $U_q[\mathfrak{osp}(2m+1|2n)^{(1)}]$, was originally introduced by H. Yamane. We provide the definition of the Drinfeld presentation $\mathcal{U}_q[\mathfrak{osp}(2m+1|2n)^{(1)}]$. To establish the isomorphism between the Drinfeld-Jimbo presentation and the Drinfeld presentation of the quantum affine superalgebra for type $\mathfrak{osp}(2m+1|2n)$, we introduce a braid group action to define quantum root vectors of the quantum superalgebra. Specifically, we present an efficient method for verifying the isomorphism between two presentations of the quantum affine superalgebra associated with the type $\mathfrak{osp}(2m+1|2n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braid group action and quantum affine superalgebra for type $\mathfrak{osp}(2m+1|2n)$ Wu, Xianghua Lin, Hongda Zhang, Honglian Quantum Algebra In this paper, we investigate the structure of the quantum affine superalgebra associated with the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m\geqslant 1$. The Drinfeld-Jimbo presentation for this algebra, denoted as $U_q[\mathfrak{osp}(2m+1|2n)^{(1)}]$, was originally introduced by H. Yamane. We provide the definition of the Drinfeld presentation $\mathcal{U}_q[\mathfrak{osp}(2m+1|2n)^{(1)}]$. To establish the isomorphism between the Drinfeld-Jimbo presentation and the Drinfeld presentation of the quantum affine superalgebra for type $\mathfrak{osp}(2m+1|2n)$, we introduce a braid group action to define quantum root vectors of the quantum superalgebra. Specifically, we present an efficient method for verifying the isomorphism between two presentations of the quantum affine superalgebra associated with the type $\mathfrak{osp}(2m+1|2n)$. |
| title | Braid group action and quantum affine superalgebra for type $\mathfrak{osp}(2m+1|2n)$ |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2410.21755 |