This article is cited in 10 papers

Scalar products in models with a $GL(3)$ trigonometric $R$-matrix: Highest coefficient

S. Z. Pakulyak^abc, E. Ragoucy^d, N. A. Slavnov<sup>e

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

Abstract: We study quantum integrable models with a $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of bilinear combinations of the highest coefficients. We show that there exist two different highest coefficients in the models with a $GL(3)$ trigonometric $R$-matrix. We obtain various representations for the highest coefficients in terms of sums over partitions. We also prove several important properties of the highest coefficients, which are necessary for evaluating the scalar products.

Keywords: nested Bethe ansatz, scalar product, highest coefficient.

Received: 18.11.2013

DOI: 10.4213/tmf8613

 English version: Theoretical and Mathematical Physics, 2014, 178:3, 314–335

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•