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Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models
by Andrii Liashyk, Stanislav Pakuliak, Eric Ragoucy
Submission summary
| Authors (as registered SciPost users): | Eric Ragoucy |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202503_00003v1 (pdf) |
| Date submitted: | 2025-03-03 16:13 |
| Submitted by: | Ragoucy, Eric |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute scalar products of off-shell Bethe vectors in models with $\mathfrak{o}_{2n+1}$ 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 $\mathfrak{gl}_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.
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Current status:
In refereeing