On Dunkl angular momenta algebra

Feigin, M. and Hakobyan, T. (2015) On Dunkl angular momenta algebra. Journal of High Energy Physics, 2015, 107. (doi: 10.1007/JHEP11(2015)107)

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We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the permutation operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincar´e-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M., and Hakobyan, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of High Energy Physics
ISSN (Online):1029-8479
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Journal of High Energy Physics 2015:107
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
569301From elliptic systems to Frobenius manifolds - 6d theories and AGTMikhail FeiginRoyal Society (ROYSOC)JP101196M&S - MATHEMATICS