From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group SL(2,C) or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147757 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation / D. Chicherin, S.E. Derkachov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 43 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862638689022115840 |
|---|---|
| author | Chicherin, D. Derkachov, S.E. Spiridonov, V.P. |
| author_facet | Chicherin, D. Derkachov, S.E. Spiridonov, V.P. |
| citation_txt | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation / D. Chicherin, S.E. Derkachov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 43 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group SL(2,C) or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional representation in one or both spaces. In this way we obtain very simple explicit formulas embracing rational and trigonometric finite-dimensional solutions of the Yang-Baxter equation. Finally, we construct these finite-dimensional solutions by means of the fusion procedure and find a nice agreement between two approaches.
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| first_indexed | 2025-11-30T23:52:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147757 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T23:52:26Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chicherin, D. Derkachov, S.E. Spiridonov, V.P. 2019-02-15T19:13:17Z 2019-02-15T19:13:17Z 2016 From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation / D. Chicherin, S.E. Derkachov, V.P. Spiridonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 43 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 82B23; 33D05 DOI:10.3842/SIGMA.2016.028 https://nasplib.isofts.kiev.ua/handle/123456789/147757 We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group SL(2,C) or Faddeev's modular double. Then we describe its restriction to an irreducible finite-dimensional representation in one or both spaces. In this way we obtain very simple explicit formulas embracing rational and trigonometric finite-dimensional solutions of the Yang-Baxter equation. Finally, we construct these finite-dimensional solutions by means of the fusion procedure and find a nice agreement between two approaches. We thank the referees for useful remarks to the paper. This work is supported by the Russian
 Science Foundation (project no. 14-11-00598). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation Article published earlier |
| spellingShingle | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation Chicherin, D. Derkachov, S.E. Spiridonov, V.P. |
| title | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation |
| title_full | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation |
| title_fullStr | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation |
| title_full_unstemmed | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation |
| title_short | From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation |
| title_sort | from principal series to finite-dimensional solutions of the yang-baxter equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147757 |
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