Braid group action and quasi-split affine iquantum groups III
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908624657317888 |
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| author | Lu, Ming Pan, Xiaolong Wang, Weiqiang Zhang, Weinan |
| author_facet | Lu, Ming Pan, Xiaolong Wang, Weiqiang Zhang, Weinan |
| contents | This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups $\widetilde{\mathbf U}^\imath$, settling the remaining type ${\rm AIII}^{(τ)}_{2r}$. This type distinguishes itself among all quasi-split affine types in having 3 relative root lengths. Various basic real and imaginary $v$-root vectors for $\widetilde{\mathbf U}^\imath$ are constructed, giving rise to affine rank one subalgebras of $\widetilde{\mathbf U}^\imath$ associated with simple roots in the finite relative root system. We establish the relations among these $v$-root vectors and show that they provide a Drinfeld presentation of $\widetilde{\mathbf U}^\imath$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_00882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Braid group action and quasi-split affine iquantum groups III Lu, Ming Pan, Xiaolong Wang, Weiqiang Zhang, Weinan Representation Theory Quantum Algebra 17B37 This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups $\widetilde{\mathbf U}^\imath$, settling the remaining type ${\rm AIII}^{(τ)}_{2r}$. This type distinguishes itself among all quasi-split affine types in having 3 relative root lengths. Various basic real and imaginary $v$-root vectors for $\widetilde{\mathbf U}^\imath$ are constructed, giving rise to affine rank one subalgebras of $\widetilde{\mathbf U}^\imath$ associated with simple roots in the finite relative root system. We establish the relations among these $v$-root vectors and show that they provide a Drinfeld presentation of $\widetilde{\mathbf U}^\imath$. |
| title | Braid group action and quasi-split affine iquantum groups III |
| topic | Representation Theory Quantum Algebra 17B37 |
| url | https://arxiv.org/abs/2511.00882 |