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Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix
Інший ID:
2010 Mathematics Subject Classification: 81R50; 17B80
DOI: http://dx.doi.org/10.3842/SIGMA.2013.058
DOI: http://dx.doi.org/10.3842/SIGMA.2013.058
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
513
Завантажень:
237
Анотація:
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.
