On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models

Abstract

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing ${\mathfrak{gl}}_3$-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.

31 pages, no figures