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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2013 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2013
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149345 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862662748773548032 |
|---|---|
| author | Belliard, S. Pakuliak, S. Ragoucy, E. Slavnov, N.A. |
| author_facet | Belliard, S. Pakuliak, S. Ragoucy, E. Slavnov, N.A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-02T13:44:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149345 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T13:44:31Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric R-Matrix Belliard, S. Pakuliak, S. Ragoucy, E. Slavnov, N.A. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149345 |
| work_keys_str_mv | AT belliards bethevectorsofquantumintegrablemodelswithgl3trigonometricrmatrix AT pakuliaks bethevectorsofquantumintegrablemodelswithgl3trigonometricrmatrix AT ragoucye bethevectorsofquantumintegrablemodelswithgl3trigonometricrmatrix AT slavnovna bethevectorsofquantumintegrablemodelswithgl3trigonometricrmatrix |