## Advanced Studies in Pure Mathematics

### 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 $U_q(sl_2)$ 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.

#### Article information

Dates
First available in Project Euclid: 21 September 2018

https://projecteuclid.org/ euclid.aspm/1537499424

Digital Object Identifier
doi:10.2969/aspm/07610095

Mathematical Reviews number (MathSciNet)
MR3837920

Zentralblatt MATH identifier
07039301

#### Citation

Chicherin, Dmitry; Spiridonov, Vyacheslav P. The hyperbolic modular double and the Yang-Baxter equation. Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, 95--123, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07610095. https://projecteuclid.org/euclid.aspm/1537499424