Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models
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...
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| Format: | Article |
| Language: | English |
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2025-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.1.023 |
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| author | A. Liashyk, S. Pakuliak, E. Ragoucy |
| author_facet | A. Liashyk, S. Pakuliak, E. Ragoucy |
| author_sort | A. Liashyk, S. Pakuliak, E. Ragoucy |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-d71bb0488c684ffcb94873f9f2c567a9 |
| institution | DOAJ |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-d71bb0488c684ffcb94873f9f2c567a92025-08-20T03:12:47ZengSciPostSciPost Physics2542-46532025-07-0119102310.21468/SciPostPhys.19.1.023Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable modelsA. Liashyk, S. Pakuliak, E. RagoucyWe 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.https://scipost.org/SciPostPhys.19.1.023 |
| spellingShingle | A. Liashyk, S. Pakuliak, E. Ragoucy Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models SciPost Physics |
| title | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| title_full | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| title_fullStr | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| title_full_unstemmed | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| title_short | Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models |
| title_sort | scalar products and norm of bethe vectors in mathfrak o 2n 1 invariant integrable models |
| url | https://scipost.org/SciPostPhys.19.1.023 |
| work_keys_str_mv | AT aliashykspakuliakeragoucy scalarproductsandnormofbethevectorsinmathfrako2n1invariantintegrablemodels |