Orthogonal Howe duality and dynamical (split) symmetric pairs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915613717299200 |
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| author | Bodish, Elijah Kalmykov, Artem |
| author_facet | Bodish, Elijah Kalmykov, Artem |
| contents | Inspired by Etingof--Varchenko's dynamical fusion, dynamical $R$-matrix, and dynamical Weyl group for Lie algebras, we introduce, for split symmetric pairs, versions of dynamical fusion, dynamical $K$-matrix, and dynamical Weyl group. We then turn to the study of $(\mathfrak{so}_{2n},O_m)$-duality and prove that the standard Knizhnik-Zamolodchikov and dynamical operators (both differential and difference) on the $\mathfrak{so}_{2n}$-side are exchanged with the symmetric pair analogs, for $O_m\subset GL_m$, on the $O_m$-side. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonal Howe duality and dynamical (split) symmetric pairs Bodish, Elijah Kalmykov, Artem Representation Theory Quantum Algebra 17B10 (Primary) 17B37, 20F36, 32G34, 53C35 (Secondary) Inspired by Etingof--Varchenko's dynamical fusion, dynamical $R$-matrix, and dynamical Weyl group for Lie algebras, we introduce, for split symmetric pairs, versions of dynamical fusion, dynamical $K$-matrix, and dynamical Weyl group. We then turn to the study of $(\mathfrak{so}_{2n},O_m)$-duality and prove that the standard Knizhnik-Zamolodchikov and dynamical operators (both differential and difference) on the $\mathfrak{so}_{2n}$-side are exchanged with the symmetric pair analogs, for $O_m\subset GL_m$, on the $O_m$-side. |
| title | Orthogonal Howe duality and dynamical (split) symmetric pairs |
| topic | Representation Theory Quantum Algebra 17B10 (Primary) 17B37, 20F36, 32G34, 53C35 (Secondary) |
| url | https://arxiv.org/abs/2405.08126 |