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 |
| Published: |
SciPost
2025-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.1.023 |
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| Summary: | 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. |
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| ISSN: | 2542-4653 |