Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe Vectors of Quantum Integrable Models with <nobr>$\mathrm{GL}(3)$</nobr> Trigonometric <nobr>$R$</nobr>-Matrix”, SIGMA, 2013, Volume 9,058, 23 pp.

This article is cited in 16 papers

Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix

Samuel Belliard^a, Stanislav Pakuliak^bcd, Eric Ragoucy^e, Nikita A. Slavnov^f

^a Université Montpellier 2, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier, France
^b Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia
^c Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Moscow reg., Russia
^d Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
^e Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie, BP 110, 74941 Annecy-le-Vieux Cedex, France
^f Steklov Mathematical Institute, Moscow, Russia

Abstract: We study quantum integrable models with $\mathrm{GL}(3)$ 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.

Keywords: nested algebraic Bethe ansatz; Bethe vector; current algebra.

MSC: 81R50; 17B80

Received: May 27, 2013; in final form September 27, 2013; Published online October 7, 2013

Language: English

DOI: 10.3842/SIGMA.2013.058