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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2309.16660 |
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| _version_ | 1866909251101786112 |
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| author | Tsuboi, Zengo |
| author_facet | Tsuboi, Zengo |
| contents | Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum affine superalgebras $U_{q}(gl(2r+1|2s)^{(2)})$, $U_{q}(gl(2r|2s+1)^{(2)})$, $U_{q}(gl(2r|2s)^{(2)})$, $U_{q}(osp(2r|2s)^{(2)})$ and the untwisted quantum affine orthosymplectic superalgebras $U_{q}(osp(2r+1|2s)^{(1)})$ and $U_{q}(osp(2r|2s)^{(1)})$ (and their Yangian counterparts, $Y(osp(2r+1|2s))$ and $Y(osp(2r|2s))$) as reductions (a kind of folding) of those associated with $U_{q}(gl(M|N)^{(1)})$. In particular, we reproduce previously proposed generating functions (difference operators) of the T-functions for the symmetric or anti-symmetric representations, and tableau sum expressions for more general representations for orthosymplectic superalgebras [arXiv:0911.5393,arXiv:0911.5390], and obtain Wronskian-type expressions (analogues of Weyl-type character formulas) for them. T-functions for spinorial representations are related to reductions of those for asymptotic limits of typical representations of $U_{q}(gl(M|N)^{(1)})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16660 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains Tsuboi, Zengo Mathematical Physics High Energy Physics - Theory Quantum Algebra Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum affine superalgebras $U_{q}(gl(2r+1|2s)^{(2)})$, $U_{q}(gl(2r|2s+1)^{(2)})$, $U_{q}(gl(2r|2s)^{(2)})$, $U_{q}(osp(2r|2s)^{(2)})$ and the untwisted quantum affine orthosymplectic superalgebras $U_{q}(osp(2r+1|2s)^{(1)})$ and $U_{q}(osp(2r|2s)^{(1)})$ (and their Yangian counterparts, $Y(osp(2r+1|2s))$ and $Y(osp(2r|2s))$) as reductions (a kind of folding) of those associated with $U_{q}(gl(M|N)^{(1)})$. In particular, we reproduce previously proposed generating functions (difference operators) of the T-functions for the symmetric or anti-symmetric representations, and tableau sum expressions for more general representations for orthosymplectic superalgebras [arXiv:0911.5393,arXiv:0911.5390], and obtain Wronskian-type expressions (analogues of Weyl-type character formulas) for them. T-functions for spinorial representations are related to reductions of those for asymptotic limits of typical representations of $U_{q}(gl(M|N)^{(1)})$. |
| title | Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2309.16660 |