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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 058, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.058 (Mi sigma841) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix

Samuel Belliarda, Stanislav Pakuliakbcd, Eric Ragoucye, Nikita 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 reg., Russia
d Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
e Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie, BP 110, 74941 Annecy-le-Vieux Cedex, France
f Steklov Mathematical Institute, Moscow, Russia
Full-text PDF (547 kB) Citations (16)
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DOI: https://doi.org/10.3842/SIGMA.2013.058
Abstract: We study quantum integrable models with $\mathrm{GL}(3)$ trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_3)$ onto intersections of different types of Borel subalgebras, we prove that the set of the nested Bethe vectors is closed under the action of the elements of the monodromy matrix.
Keywords: nested algebraic Bethe ansatz; Bethe vector; current algebra.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00980-a
11-01-00440
National Research University Higher School of Economics 12-09-0064
Agence Nationale de la Recherche 2010-BLAN-0120-02
Ministry of Education and Science of the Russian Federation SS-4612.2012.1
Work of S.P. was supported in part by RFBR grant 11-01-00980-a and grant of Scientific Foundation of NRU HSE 12-09-0064. 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, SS-4612.2012.1.
Received: May 27, 2013; in final form September 27, 2013; Published online October 7, 2013
Bibliographic databases:
Document Type: Article
MSC: 81R50; 17B80
Language: English
Citation: Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix”, SIGMA, 9 (2013), 058, 23 pp.
Citation in format AMSBIB
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