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From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
Інший ID:
2010 Mathematics Subject Classification: 81R50; 82B23; 33D05
DOI:10.3842/SIGMA.2016.028
DOI:10.3842/SIGMA.2016.028
Посилання:
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.
Підтримка:
We thank the referees for useful remarks to the paper. This work is supported by the Russian
Science Foundation (project no. 14-11-00598).
Дата:
2016
Переглядів:
516
Завантажень:
249
Анотація:
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.
