Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “<nobr>${\rm GL}(3)$</nobr>-Based Quantum Integrable Composite Models. I. Bethe Vectors”, SIGMA, 2015, Volume 11,063, 20 pp.

This article is cited in 19 papers

${\rm GL}(3)$-Based Quantum Integrable Composite Models. I. Bethe Vectors

Stanislav Pakuliak^abc, Eric Ragoucy^d, Nikita A. Slavnov^e

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

Abstract: We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the ${\rm GL}(3)$-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik–Zamolodchikov equation.

Keywords: Bethe ansatz; quantum affine algebras, composite models.

MSC: 17B37; 81R50

Received: February 18, 2015; in final form July 22, 2015; Published online July 31, 2015

Language: English

DOI: 10.3842/SIGMA.2015.063