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.
Published inInternational Mathematics Research Notices
Pages10959 - 10986
CitationVESELOV, A.P. and SERGEEV, A.N., 2015. Dunkl operators at infinity and Calogero-Moser systems. International Mathematics Research Notices, 21, pp.10959-10986.
PublisherOxford University Press (© The Authors 2015)
VersionVoR (Version of Record)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
NotesThis is an Open Access article distributed by Oxford University Press under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. It was originally published at: http://dx.doi.org/10.1093/imrn/rnv002