Abstract
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection 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 Poincaré-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 subalge-bra 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.
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Feigin, M., Hakobyan, T. On Dunkl angular momenta algebra. J. High Energ. Phys. 2015, 107 (2015). https://doi.org/10.1007/JHEP11(2015)107
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DOI: https://doi.org/10.1007/JHEP11(2015)107