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arXiv · 1411.7595

From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation

Dmitry Chicherin·Sergey E. Derkachov·Vyacheslav P. Spiridonov
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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.

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BibTeXRIS

Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav P. Spiridonov. 2014-11-27. From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation. https://doi.org/10.3842/sigma.2016.028

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