Zamolodchikov-Faddeev algebra in Ruijsenaars hyperbolic model

Ruijsenaars hyperbolic model was discovered in the mid-1980s as a many-body interacting system describing solitons trajectories for the famous sine-Gordon equation. The Hamiltonians of the quantum problem are multi-dimensional difference operators with shifts of coordinates in imaginary direction, and in 2012 Hällnas and Ruijsenaars managed to explicitly construct their eigenfunctions. Recently in the joint work with Derkachov, Kharchev and Khoroshkin we proved several properties of these eigenfunctions, including orthogonality, completeness and some symmetries. In the talk I will discuss the main tools we used and how they are related to the famous Zamolodchikov-Faddeev algebra.