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Dunkl operators at infinity and Calogero-Moser systems

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posted on 18.03.2015, 09:26 authored by Alexander VeselovAlexander 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

Volume

2015

Issue

21

Pages

10959 - 10986

Citation

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

05/01/2015

Publication date

2015-02-02

Notes

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/rnv002

ISSN

1073-7928

eISSN

1687-0247

Language

en

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