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TMF, 2014, Volume 178, Number 3, Pages 363–389 (Mi tmf8613)  

This article is cited in 7 scientific papers (total in 7 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

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


DOI: https://doi.org/10.4213/tmf8613

Full text: PDF file (666 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 178:3, 314–335

Bibliographic databases:

Received: 18.11.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case”, Theoret. and Math. Phys., 180:1 (2014), 795–814  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. J. Caetano, T. Fleury, “Three-point functions and $\mathfrak{su}(1|1)$ spin chains”, J. High Energy Phys., 2014, no. 9, 173  crossref  mathscinet  isi  scopus
    3. Arthur Hutsalyuk, Andrii Liashyk, Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models”, SIGMA, 12 (2016), 099, 22 pp.  mathnet  crossref  mathscinet  elib
    4. K. K. Kozlowski, E. Ragoucy, “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288  crossref  mathscinet  zmath  isi  elib  scopus
    5. N. Gromov, F. Levkovich-Maslyuk, G. Sizov, “New construction of eigenstates and separation of variables for $\mathrm{SU}(N)$ quantum spin chains”, J. High Energy Phys., 2017, no. 9, 111  crossref  mathscinet  zmath  isi  scopus
    6. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_m)$”, SciPost Phys., 4:1 (2018), 006  crossref  isi
    7. Liashyk A., Pakuliak S.Z., Ragoucy E., Slavnov N.A., “New Symmetries of Gl(N)-Invariant Bethe Vectors”, J. Stat. Mech.-Theory Exp., 2019, 044001  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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