New elliptic solutions of the Yang-Baxter equation

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

Published 2014-12-10Version 1

We consider finite-dimensional reductions of the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra, which is described by an integral operator with an elliptic hypergeometric kernel. 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 reproduced using the fusion formalism.