Bethe Vectors in Quantum Integrable Models with Classical Symmetries
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917180450275328 |
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| author | Liashyk, A. Pakuliak, S. Ragoucy, E. |
| author_facet | Liashyk, A. Pakuliak, S. Ragoucy, E. |
| contents | The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the off-shell Bethe vectors indeed become on-shell when the Bethe equations are obeyed.
Then, we show that some properties for these off-shell Bethe vectors, such as the action formulas of monodromy entries on these vectors, their rectangular recurrence relations and their coproduct formula, are a consequence of our definition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00713 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bethe Vectors in Quantum Integrable Models with Classical Symmetries Liashyk, A. Pakuliak, S. Ragoucy, E. Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems 17B80, 82B23, 17B37 The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the off-shell Bethe vectors indeed become on-shell when the Bethe equations are obeyed. Then, we show that some properties for these off-shell Bethe vectors, such as the action formulas of monodromy entries on these vectors, their rectangular recurrence relations and their coproduct formula, are a consequence of our definition. |
| title | Bethe Vectors in Quantum Integrable Models with Classical Symmetries |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems 17B80, 82B23, 17B37 |
| url | https://arxiv.org/abs/2601.00713 |