The hyperbolic modular double and the Yang-Baxter equation

Abstract

We construct a hyperbolic modular double -- an algebra lying in between the Faddeev modular double for $U_q(s{l}_2)$ and the elliptic modular double. The intertwining operator for this algebra leads to an integral operator solution of the Yang-Baxter equation associated with a generalized Faddeev-Volkov lattice model introduced by the second author. We describe also the L-operator and finite-dimensional R-matrices for this model.

29 pages, 4 figures. v3: references added, to appear in Advanced Studies in Pure Mathematics

References in corpus (5)

• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Yang-Baxter R operators and parameter permutations
• Integrable light-cone lattice discretizations from the universal R-matrix
• New elliptic solutions of the Yang-Baxter equation

Cited by in corpus (2)

• The Endless Beta Integrals
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities