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| Format: | Preprint |
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2021
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| Online Access: | https://arxiv.org/abs/2106.08931 |
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| _version_ | 1866910516381745152 |
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| author | Tsuboi, Zengo |
| author_facet | Tsuboi, Zengo |
| contents | It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(2)})$ and the non-twisted quantum affine algebra $U_{q}(so(2r+1)^{(1)})$, we proposed, in the previous paper [arXiv:1109.5524], a Wronskian solution of the T-system for $U_{q}(so(2r+1)^{(1)})$ as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(1)})$. In this paper, we elaborate on this solution, and give a proof missing in [arXiv:1109.5524]. In particular, we explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum Jacobi-Trudi) type determinant solution known in [arXiv:hep-th/9506167]. We also propose Wronskian-type expressions of T-functions (eigenvalues of transfer matrices) labeled by non-rectangular Young diagrams, which are quantum affine algebra analogues of the Weyl character formula for $so(2r+1)$. We show that T-functions for spinorial representations of $U_{q}(so(2r+1)^{(1)})$ are related to reductions of T-functions for asymptotic typical representations of $U_{q}(gl(2r|1)^{(1)})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_08931 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system Tsuboi, Zengo Mathematical Physics Quantum Algebra It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(2)})$ and the non-twisted quantum affine algebra $U_{q}(so(2r+1)^{(1)})$, we proposed, in the previous paper [arXiv:1109.5524], a Wronskian solution of the T-system for $U_{q}(so(2r+1)^{(1)})$ as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra $U_{q}(gl(2r|1)^{(1)})$. In this paper, we elaborate on this solution, and give a proof missing in [arXiv:1109.5524]. In particular, we explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum Jacobi-Trudi) type determinant solution known in [arXiv:hep-th/9506167]. We also propose Wronskian-type expressions of T-functions (eigenvalues of transfer matrices) labeled by non-rectangular Young diagrams, which are quantum affine algebra analogues of the Weyl character formula for $so(2r+1)$. We show that T-functions for spinorial representations of $U_{q}(so(2r+1)^{(1)})$ are related to reductions of T-functions for asymptotic typical representations of $U_{q}(gl(2r|1)^{(1)})$. |
| title | Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system |
| topic | Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2106.08931 |