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

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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. Pakulyak^abc, E. Ragoucy^d, N. A. Slavnov^e

^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

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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:

A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “New symmetries of gl(n)-invariant Bethe vectors”, J. Stat. Mech.-Theory Exp., 2019, 044001
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
Stanislav Pakuliak, Eric Ragoucy, Nikita Slavnov, “Nested Algebraic Bethe Ansatz in integrable models: recent results”, SciPost Phys. Lect. Notes, 2018
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
Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe vectors for models based on the super-Yangian $Y(gl(m|n))$”, J. Integrab. Syst., 2 (2017), 1–31
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.
K. K. Kozlowski, E. Ragoucy, “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288
N. A. Slavnov, “Scalar products in $GL(3)$-based models with trigonometric $R$-matrix. Determinant representation”, J. Stat. Mech., 2015:3 (2015), 3019–25
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
J. Caetano, T. Fleury, “Three-point functions and $\mathfrak{su}(1|1)$ spin chains”, J. High Energy Phys., 2014, no. 9, 173

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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