Dunkl operators at infinity and Calogero-Moser systems

2015-03-18T09:26:34Z (GMT) by Alexander Veselov A.N. Sergeev
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.