Dunkl operators at infinity and Calogero–Moser systems

We define the Dunkl and Dunkl–Heckman operators in infinite number of variables and use them to construct the quantum integrals of the Calogero–Moser–Sutherland problems at infinity. As a corollary we have a simple proof of integrability of the deformed quantum CMS systems related to classical Lie superalgebras. The talk is based on a joint work with A. N. Sergeev.