# On Bethe vectors in $$\mathfrak{g}{\mathfrak{l}}_3$$ -invariant integrable models

Journal of High Energy Physics, Jun 2018

Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $$\mathfrak{g}{\mathfrak{l}}_3$$-invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters. They thus do become on-shell vectors provided the system of Bethe equations is fulfilled.

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A. Liashyk, N. A. Slavnov. On Bethe vectors in $$\mathfrak{g}{\mathfrak{l}}_3$$ -invariant integrable models, Journal of High Energy Physics, 2018, 18, DOI: 10.1007/JHEP06(2018)018