Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Liashyk, A. Pakuliak, S. Ragoucy, E. |
| author_facet | Liashyk, A. Pakuliak, S. Ragoucy, E. |
| contents | We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients. We prove some recurrence relations and a residue theorem for these highest coefficients, and prove that they are consistent with the reduction to $gl_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models Liashyk, A. Pakuliak, S. Ragoucy, E. Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients. We prove some recurrence relations and a residue theorem for these highest coefficients, and prove that they are consistent with the reduction to $gl_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant. |
| title | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.01578 |