On integrable deformations of the Cherednik model

In this paper, we provide the [Formula: see text]-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version. In all three cases, we solve the sufficient condition of integrability by using the [Formula: see text]-model formalism. We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.