This article is cited in 8 papers

Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case

S. Z. Pakulyak^abc, E. Ragoucy^de, N. A. Slavnov<sup>f

a</sup> Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
^b Institute of Theoretical and Experimental Physics, Moscow, Russia
^c Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
^d CNRS — Université de Savoie, Annecy-le-Vieux, France
^e Laboratoire d'Annecy-le-Vieux de Physique Théorique
^f Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We study quantum integrable models with the $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz and obtain an explicit representation for a scalar product of generic Bethe vectors in terms of a sum over partitions of Bethe parameters. This representation generalizes the known formula for scalar products in models with the $GL(3)$-invariant $R$-matrix.

Keywords: nested Bethe ansatz, Bethe vector, scalar products.

Received: 12.02.2014

DOI: 10.4213/tmf8651

 English version: Theoretical and Mathematical Physics, 2014, 180:1, 795–814

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