The Calogero-Moser integrable model describes a system of pairwise interacting particles on a line or a circle with inverse square distance potential. The corresponding potential is naturally associated with the root system of type A. Integrable generalisations for any root system were introduced by Olshanetsky and Perelomov in the end of 70's. The quantum integrable generalisations for configurations not being root systems were discovered in the works of  Chalykh, Feigin and Veselov in the end of 90's. In 2012 these and further deformed Calogero-Moser systems were studied from the point of view of Cherednik algebras by Feigin.

      

The quantum matrix version of the Calogero-Moser model appeared in the works of Ha and Haldane in the early 90's. The deformed quantum matrix version in the rational case was introduced by Chalykh, Goncharenko and Veselov in 1999. We obtain these examples as well as various generalisations by making use of the representation theory of Cherednik algebras. Based on our joint work with M. Feigin.