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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 findan exact common eigenfunction for a generalization of Ruijsenaars analyticdifference operators that gives, as special cases, many different kernelfunctions; in particular, we find kernel functions for Chalykh-Feigin-Veselov-Sergeev-type deformations of such difference operators whichgeneralize known kernel functions for the Ruijsenaars models. We also discusspossible applications of our results.

Source identities and kernel functions for deformed (quantum) Ruijsenaars models