Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 063, 20 pages      arXiv:1501.07566

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

Stanislav Pakuliak abc, Eric Ragoucy d and Nikita A. Slavnov e
a) Institute of Theoretical & Experimental Physics, 117259 Moscow, Russia
b) Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
c) Moscow Institute of Physics and Technology, 141700, Dolgoprudny, 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

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

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.

Key words: Bethe ansatz; quantum affine algebras, composite models.

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