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

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 $g{l}_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.

arXiv comment38 pages; introduction improved nd conclusion added; more explanations on the gl(n) reduction

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Cited by in corpus (1)

• Effective Bethe Ansatz for Spin-1 Non-integrable Models