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arXiv · 2503.01578

Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models

A. Liashyk·S. Pakuliak·E. Ragoucy
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Abstract

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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A. Liashyk, S. Pakuliak, E. Ragoucy. 2025-03-03. Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models. https://doi.org/10.21468/scipostphys.19.1.023

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