Braid group action and quasi-split affine $\imath$quantum groups II: higher rank
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917685711863808 |
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| author | Lu, Ming Wang, Weiqiang Zhang, Weinan |
| author_facet | Lu, Ming Wang, Weiqiang Zhang, Weinan |
| contents | This paper studies quantum symmetric pairs $(\widetilde{\mathbf U}, \widetilde{\mathbf U}^\imath )$ associated with quasi-split Satake diagrams of affine type $A_{2r-1}, D_r, E_{6}$ with a nontrivial diagram involution fixing the affine simple node. Various real and imaginary root vectors for the universal $\imath$quantum groups $\widetilde{\mathbf U}^\imath$ are constructed with the help of the relative braid group action, and they are used to construct affine rank one subalgebras of $\widetilde{\mathbf U}^\imath$. We then establish relations among real and imaginary root vectors in different affine rank one subalgebras and use them to give a Drinfeld type presentation of $\widetilde{\mathbf U}^\imath$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10299 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Braid group action and quasi-split affine $\imath$quantum groups II: higher rank Lu, Ming Wang, Weiqiang Zhang, Weinan Quantum Algebra Representation Theory This paper studies quantum symmetric pairs $(\widetilde{\mathbf U}, \widetilde{\mathbf U}^\imath )$ associated with quasi-split Satake diagrams of affine type $A_{2r-1}, D_r, E_{6}$ with a nontrivial diagram involution fixing the affine simple node. Various real and imaginary root vectors for the universal $\imath$quantum groups $\widetilde{\mathbf U}^\imath$ are constructed with the help of the relative braid group action, and they are used to construct affine rank one subalgebras of $\widetilde{\mathbf U}^\imath$. We then establish relations among real and imaginary root vectors in different affine rank one subalgebras and use them to give a Drinfeld type presentation of $\widetilde{\mathbf U}^\imath$. |
| title | Braid group action and quasi-split affine $\imath$quantum groups II: higher rank |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2311.10299 |