Integrable modules over quantum symmetric pair coideal subalgebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918286848950272 |
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| author | Watanabe, Hideya |
| author_facet | Watanabe, Hideya |
| contents | We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is integrable when restricted to an $\imath$quantum group. As an application, we show that the space of matrix coefficients of all simple integrable modules over an $\imath$quantum group of finite type with specific parameters coincides with Bao-Song's coordinate ring of the $\imath$quantum group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable modules over quantum symmetric pair coideal subalgebras Watanabe, Hideya Quantum Algebra Representation Theory 17B10 (Primary) 17B37 (Secondary) We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is integrable when restricted to an $\imath$quantum group. As an application, we show that the space of matrix coefficients of all simple integrable modules over an $\imath$quantum group of finite type with specific parameters coincides with Bao-Song's coordinate ring of the $\imath$quantum group. |
| title | Integrable modules over quantum symmetric pair coideal subalgebras |
| topic | Quantum Algebra Representation Theory 17B10 (Primary) 17B37 (Secondary) |
| url | https://arxiv.org/abs/2407.07280 |