New elliptic solutions of the Yang-Baxter equation

TL;DR

This paper introduces new elliptic solutions to the Yang-Baxter equation derived from finite-dimensional reductions of an integral operator with an elliptic hypergeometric kernel, connecting to known models and expanding solution space.

Contribution

It provides a novel, compact formula for elliptic solutions of the Yang-Baxter equation based on finite-dimensional representations of the elliptic modular double.

Findings

Reproduces Baxter's R-matrix for the 8-vertex model

Derives new elliptic solutions via fusion formalism

Connects solutions to elliptic modular double representations

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.