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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 3, Pages 363–389
DOI: https://doi.org/10.4213/tmf8613 (Mi tmf8613) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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

S. Z. Pakulyakabc, E. Ragoucyd, N. A. Slavnove

a 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
Full-text PDF (666 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf8613
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.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00962_а
11-01-00440_a
13-01-12405-офи_м
National Research University Higher School of Economics 12-09-0064
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 НШ-2484.2014.1
Received: 18.11.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 3, Pages 314–335
DOI: https://doi.org/10.1007/s11232-014-0145-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with a $GL(3)$ trigonometric $R$-matrix: Highest coefficient”, TMF, 178:3 (2014), 363–389; Theoret. and Math. Phys., 178:3 (2014), 314–335
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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