Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912323144253440 |
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| author | Lu, Kang Wang, Weiqiang Zhang, Weinan |
| author_facet | Lu, Kang Wang, Weiqiang Zhang, Weinan |
| contents | We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations Lu, Kang Wang, Weiqiang Zhang, Weinan Quantum Algebra Mathematical Physics Representation Theory 17B37 We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation. |
| title | Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations |
| topic | Quantum Algebra Mathematical Physics Representation Theory 17B37 |
| url | https://arxiv.org/abs/2406.05067 |