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 (CMS) problems at infinity. As a corollary, we have a simple proof of integrability of the deformed quantum CMS systems related to classical Lie superalgebras. We show how this naturally leads to a quantum version of the Moser matrix, which in the deformed case was not known before. [ABSTRACT FROM AUTHOR]