Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910779859533824 |
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| author | Lu, Kang |
| author_facet | Lu, Kang |
| contents | By employing Gauss decomposition, we establish a direct and explicit isomorphism between the twisted $q$-Yangians (in R-matrix presentation) and affine $\imath$quantum groups (in current presentation) associated to symmetric pair of type AI introduced by Molev-Ragoucy-Sorba and Lu-Wang, respectively. As a corollary, we obtain a PBW type basis for affine $\imath$quantum groups of type AI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI Lu, Kang Quantum Algebra Mathematical Physics Representation Theory 17B37 By employing Gauss decomposition, we establish a direct and explicit isomorphism between the twisted $q$-Yangians (in R-matrix presentation) and affine $\imath$quantum groups (in current presentation) associated to symmetric pair of type AI introduced by Molev-Ragoucy-Sorba and Lu-Wang, respectively. As a corollary, we obtain a PBW type basis for affine $\imath$quantum groups of type AI. |
| title | Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI |
| topic | Quantum Algebra Mathematical Physics Representation Theory 17B37 |
| url | https://arxiv.org/abs/2308.12484 |