Twisted q-Yangians and Sklyanin determinants
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910876327477248 |
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| author | Jing, Naihuan Zhang, Jian |
| author_facet | Jing, Naihuan Zhang, Jian |
| contents | $q$-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the $q$-Yangian algebras. This viewpoint enables us to investigate the invariant theory of quantum affine algebras and their twisted versions. We introduce the twisted Sklyanin determinant for twisted quantum affine algebras and establish various identities for the Sklyanin determinants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted q-Yangians and Sklyanin determinants Jing, Naihuan Zhang, Jian Quantum Algebra Primary: 17B37, Secondary: 17B10, 81R50, 14M17, 15A15, 13A50 $q$-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the $q$-Yangian algebras. This viewpoint enables us to investigate the invariant theory of quantum affine algebras and their twisted versions. We introduce the twisted Sklyanin determinant for twisted quantum affine algebras and establish various identities for the Sklyanin determinants. |
| title | Twisted q-Yangians and Sklyanin determinants |
| topic | Quantum Algebra Primary: 17B37, Secondary: 17B10, 81R50, 14M17, 15A15, 13A50 |
| url | https://arxiv.org/abs/2408.04340 |