Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix

We study quantum integrable models with 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 Uq(glˆ₃) onto intersections of different typ...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2013
Main Authors: Belliard, S., Pakuliak, S., Ragoucy, E., Slavnov, N.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2013
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149345
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matri / S. Belliard, S. Pakuliak, E. Ragoucy, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 26 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149345
record_format dspace
spelling Belliard, S.
Pakuliak, S.
Ragoucy, E.
Slavnov, N.A.
2019-02-21T07:05:43Z
2019-02-21T07:05:43Z
2013
Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matri / S. Belliard, S. Pakuliak, E. Ragoucy, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 26 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81R50; 17B80
DOI: http://dx.doi.org/10.3842/SIGMA.2013.058
https://nasplib.isofts.kiev.ua/handle/123456789/149345
We study quantum integrable models with 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 Uq(glˆ₃) 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.
This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html. 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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
spellingShingle Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
Belliard, S.
Pakuliak, S.
Ragoucy, E.
Slavnov, N.A.
title_short Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
title_full Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
title_fullStr Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
title_full_unstemmed Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
title_sort bethe vectors of quantum integrable models with gl(3) trigonometric r-matrix
author Belliard, S.
Pakuliak, S.
Ragoucy, E.
Slavnov, N.A.
author_facet Belliard, S.
Pakuliak, S.
Ragoucy, E.
Slavnov, N.A.
publishDate 2013
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We study quantum integrable models with 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 Uq(glˆ₃) 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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149345
citation_txt Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matri / S. Belliard, S. Pakuliak, E. Ragoucy, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 26 назв. — англ.
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AT slavnovna bethevectorsofquantumintegrablemodelswithgl3trigonometricrmatrix
first_indexed 2025-12-02T13:44:31Z
last_indexed 2025-12-02T13:44:31Z
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