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

Symmetry Integrability and Geometry-Methods and Applications

article

Samuel Belliard¹  Stanislav Pakuliak²  Eric Ragoucy⁵  Nikita A. Slavnov⁶ 

[1] Université Montpellier 2, Laboratoire Charles Coulomb;Laboratory of Theoretical Physics;Moscow Institute of Physics and Technology;Institute of Theoretical and Experimental Physics;Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie;Steklov Mathematical Institute

关键词: nested algebraic Bethe ansatz;    Bethe vector;    current algebra;   

DOI  :  10.3842/SIGMA.2013.058

来源: National Academy of Science of Ukraine

【 摘 要 】

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 monodromy matrix.

【 授权许可】

Unknown