Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix

Abstract

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz.Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine algebra $U_q(widehat{mathfrak{gl}}_3)$ onto intersections of different types of Borel subalgebras, we prove that the set of the nested Bethe vectors is closed under the action of the elements of the monodromymatrix.

Keywords

• nested algebraic Bethe ansatz
• Bethe vector
• current algebra