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

SIGMA 11 (2015), 064, 18 pages      arXiv:1502.01966      https://doi.org/10.3842/SIGMA.2015.064

### ${\rm GL}(3)$-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators

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

Abstract
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the ${\rm GL}(3)$-invariant $R$-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial monodromy matrices. Assuming that the last ones can be expanded into series with respect to the inverse spectral parameter we calculate matrix elements of the local operators in the basis of the transfer matrix eigenstates. We obtain determinant representations for these matrix elements. Thus, we solve the inverse scattering problem in a weak sense.

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

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