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arXiv · 1412.3383

New elliptic solutions of the Yang-Baxter equation

D. Chicherin·S. E. Derkachov·V. P. Spiridonov
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Abstract

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism.

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D. Chicherin, S. E. Derkachov, V. P. Spiridonov. 2014-12-10. New elliptic solutions of the Yang-Baxter equation. https://doi.org/10.1007/s00220-016-2590-2

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