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This article is cited in 8 scientific papers (total in 8 papers)
From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation
Dmitry Chicherina, Sergey E. Derkachovb, Vyacheslav P. Spiridonovc a LAPTH, UMR 5108 du CNRS, associée à l'Université de Savoie, Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, France
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
c Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, 141980, Russia
Abstract:
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 $\mathrm{SL}(2,\mathbb{C})$ 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.
Keywords:
Yang–Baxter equation; principal series; modular double; fusion.
Received: November 17, 2015; in final form March 4, 2016; Published online March 11, 2016
Citation:
Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov, “From Principal Series to Finite-Dimensional Solutions of the Yang–Baxter Equation”, SIGMA, 12 (2016), 028, 34 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1110 https://www.mathnet.ru/eng/sigma/v12/p28
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