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arXiv:2503.01578 · SciPost Physics

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

Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak, E. Ragoucy

Published Jul 18, 2025• 3 citations
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Abstract

We compute scalar products of off-shell Bethe vectors in models with \mathfrak{o}_{2n+1} 𝔬 2 n + 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{g}\mathfrak{l}_n 𝔤 𝔩 n invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.

DOI
10.21468/scipostphys.19.1.023

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