The hyperbolic modular double and the Yang-Baxter equation

Chicherin, Dmitry; Spiridonov, Vyacheslav P.

doi:10.2969/aspm/07610095

VOL. 76 | 2018 The hyperbolic modular double and the Yang-Baxter equation

Dmitry Chicherin, Vyacheslav P. Spiridonov

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

Adv. Stud. Pure Math., 2018: 95-123 (2018) DOI: 10.2969/aspm/07610095

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.