Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

We consider the relativistic generalization of the quantum A _N-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh–Feigin–Veselov–Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.