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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| Datum: | 2016 |
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| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147757 |
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| Zitieren: | 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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irk-123456789-1477572019-02-16T01:25:32Z From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation Chicherin, D. Derkachov, S.E. Spiridonov, V.P. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147757 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Chicherin, D. Derkachov, S.E. Spiridonov, V.P. |
| spellingShingle |
Chicherin, D. Derkachov, S.E. Spiridonov, V.P. From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chicherin, D. Derkachov, S.E. Spiridonov, V.P. |
| author_sort |
Chicherin, D. |
| title |
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_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_sort |
from principal series to finite-dimensional solutions of the yang-baxter equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147757 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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