Dunkl operators at infinity and Calogero-Moser systems
Mathematical Physics
2013-12-10 v2 math.MP
Abstract
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. We show how this naturally leads to a quantum version of the Moser matrix, which in the deformed case was not known before.
Cite
@article{arxiv.1311.0853,
title = {Dunkl operators at infinity and Calogero-Moser systems},
author = {A. N. Sergeev and A. P. Veselov},
journal= {arXiv preprint arXiv:1311.0853},
year = {2013}
}
Comments
22 pages. Corrected version with minor changes