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Theoretical and Mathematical Physics

, Volume 178, Issue 3, pp 314–335 | Cite as

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

  • S. Z. PakuliakEmail author
  • E. Ragoucy
  • N. A. Slavnov
Article

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 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubna, Moscow OblastRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudny, Moscow OblastRussia
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowRussia
  4. 4.Laboratoire d’Annecy-le-Vieux de Physique ThéoriqueCNRS-Université de SavoieAnnecy-le-VieuxFrance
  5. 5.Steklov Mathematical InstituteRASMoscowRussia

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