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TMF, 2014, Volume 180, Number 1, Pages 51–71 (Mi tmf8651)  

This article is cited in 5 scientific papers (total in 5 papers)

Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case

S. Z. Pakulyakabc, E. Ragoucyde, N. A. Slavnovf

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

Abstract: We study quantum integrable models with the $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz and obtain an explicit representation for a scalar product of generic Bethe vectors in terms of a sum over partitions of Bethe parameters. This representation generalizes the known formula for scalar products in models with the $GL(3)$-invariant $R$-matrix.

Keywords: nested Bethe ansatz, Bethe vector, scalar products

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00474
13-01-12405-офи_м
14-01-00860_а
National Research University Higher School of Economics
Agence Nationale de la Recherche 2010-BLAN-0120-02
Russian Academy of Sciences - Federal Agency for Scientific Organizations П-19


DOI: https://doi.org/10.4213/tmf8651

Full text: PDF file (624 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 180:1, 795–814

Bibliographic databases:

Received: 12.02.2014

Citation: S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case”, TMF, 180:1 (2014), 51–71; Theoret. and Math. Phys., 180:1 (2014), 795–814

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. 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
    2. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in models with ${\mathfrak{gl}}(2| 1)$ symmetry 1. Super-analog of Reshetikhin formula”, J. Phys. A-Math. Theor., 49:45 (2016), 454005, 1–28  crossref  mathscinet  isi  scopus
    3. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in models with $\mathfrak{g}\mathfrak{l}(2|1)$ symmetry 2. Determinant representation”, J. Phys. A-Math. Theor., 50:3 (2017), 034004  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry”, Nucl. Phys. B, 923 (2017), 277–311  crossref  mathscinet  zmath  isi  scopus
    5. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_n)$”, SciPost Phys., 4:1 (2018), 006  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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