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J. Stat. Mech., 2012, Volume 2012, Number 9, 9003, 17 pages (Mi jsm6)  

Highest coefficient of scalar products in $SU(3)$-invariant integrable models

S. Belliarda, S. Pakuliakbcd, E. Ragoucye, N. A. Slavnovf

a Université Montpellier 2, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier, France
b Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia
c Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Moscow region, Russia
d Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow region, Russia
e Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie, BP 110, F-74941 Annecy-le-Vieux Cedex, France
f Steklov Mathematical Institute, Moscow, Russia

Abstract: We study $SU(3)$-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00980-a
11-01-00440
11-01-12037-ofi-m
National Research University Higher School of Economics 12-09-0064
Federal Agency for Science and Innovations of Russian Federation 14.740.11.0347
Agence Nationale de la Recherche 2010-BLAN-0120-02
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation SS-4612.2012.1
The work of S P was supported in part by RFBR grant 11-01-00980-a, a grant of the Scientific Foundation of NRU HSE 12-09-0064 and a grant of FAST RF 14.740.11.0347. E R was supported by ANR Project DIADEMS (Programme Blanc ANR SIMI1 2010-BLAN-0120-02). N A S was supported by the Program of RAS Basic Problems of the Nonlinear Dynamics, RFBR-11-01-00440, RFBR-11-01-12037-ofi-m, SS-4612.2012.1.


DOI: https://doi.org/10.1088/1742-5468/2012/09/P09003


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Received: 05.07.2012
Accepted:12.08.2012
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