A Q-operator for open spin chains II: boundary factorization
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917619456540672 |
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| author | Cooper, Alec Vlaar, Bart Weston, Robert |
| author_facet | Cooper, Alec Vlaar, Bart Weston, Robert |
| contents | One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang-Baxter equation associated to particular infinite-dimensional representations). To have such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang-Baxter equation) associated to these representations. In the case of quantum affine $\mathfrak{sl}_2$ and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_03997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Q-operator for open spin chains II: boundary factorization Cooper, Alec Vlaar, Bart Weston, Robert Mathematical Physics Quantum Algebra Representation Theory Primary 81R10, 81R12, 81R50, Secondary 16T05, 16T25, 39B42 One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang-Baxter equation associated to particular infinite-dimensional representations). To have such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang-Baxter equation) associated to these representations. In the case of quantum affine $\mathfrak{sl}_2$ and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras. |
| title | A Q-operator for open spin chains II: boundary factorization |
| topic | Mathematical Physics Quantum Algebra Representation Theory Primary 81R10, 81R12, 81R50, Secondary 16T05, 16T25, 39B42 |
| url | https://arxiv.org/abs/2301.03997 |