Dunkl operators at infinity and Calogero-Moser systems
journal contribution
posted on 2015-03-18, 09:26 authored by Alexander VeselovAlexander Veselov, A.N. SergeevWe 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.
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School
- Science
Department
- Mathematical Sciences
Published in
International Mathematics Research NoticesVolume
2015Issue
21Pages
10959 - 10986Citation
VESELOV, A.P. and SERGEEV, A.N., 2015. Dunkl operators at infinity and Calogero-Moser systems. International Mathematics Research Notices, 21, pp.10959-10986.Publisher
Oxford University Press (© The Authors 2015)Version
- VoR (Version of Record)
Publisher statement
This 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/Acceptance date
2015-01-05Publication date
2015-02-02Notes
This 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/rnv002ISSN
1073-7928eISSN
1687-0247Publisher version
Language
- en
