Quantum supersymmetric pairs and $\imath$Schur duality of type AIII
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911115032657920 |
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| author | Shen, Yaolong |
| author_facet | Shen, Yaolong |
| contents | We construct quantum supersymmetric pairs $({\bold U},{\bold U}^\imath)$ of type AIII and elucidate their fundamental properties. An $\imath$Schur duality between the $\imath$quantum supergroup ${\bold U}^\imath$ and the Hecke algebra of type B acting on a tensor space is established, providing a super generalization of the $\imath$Schur duality of type AIII. Additionally, we construct a (quasi) $K$-matrix for arbitrary parameters, which facilitates the realization of the Hecke algebra action on the tensor space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01233 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum supersymmetric pairs and $\imath$Schur duality of type AIII Shen, Yaolong Quantum Algebra Representation Theory We construct quantum supersymmetric pairs $({\bold U},{\bold U}^\imath)$ of type AIII and elucidate their fundamental properties. An $\imath$Schur duality between the $\imath$quantum supergroup ${\bold U}^\imath$ and the Hecke algebra of type B acting on a tensor space is established, providing a super generalization of the $\imath$Schur duality of type AIII. Additionally, we construct a (quasi) $K$-matrix for arbitrary parameters, which facilitates the realization of the Hecke algebra action on the tensor space. |
| title | Quantum supersymmetric pairs and $\imath$Schur duality of type AIII |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2210.01233 |