New elliptic solutions of the Yang-Baxter equation

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.

34 pages, to appear in Commun. Math. Phys

References in corpus (4)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Essays on the theory of elliptic hypergeometric functions
• Yang-Baxter R operators and parameter permutations
• Sklyanin invariant integration

Cited by in corpus (7)

• Surface defects and elliptic quantum groups
• The star-triangle relation and 3d superconformal indices
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• The rarefied elliptic Bailey lemma and the Yang-Baxter equation
• The hyperbolic modular double and the Yang-Baxter equation
• Q-operators for higher spin eight vertex models with a rational anisotropy parameter
• Matrix factorization for solutions of the Yang-Baxter equation