From principal series to finite-dimensional solutions of the Yang-Baxter equation

D. Chicherin, S. E. Derkachov, V. P. Spiridonov

Published 2014-11-27Version 1

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.