Abstract
The spherical reduction of the rational Calogero model (of type A n−1 and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n−2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a spherical tetrahexahedron. A complete set of independent conserved charges and of Hamiltonian intertwiners is constructed, and their algebra is elucidated. They arise from the ring of polynomials in Dunkl-deformed angular momenta, by classifying the subspaces invariant and antiinvariant under all Weyl reflections, respectively.
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Correa, F., Lechtenfeld, O. The tetrahexahedric angular Calogero model. J. High Energ. Phys. 2015, 191 (2015). https://doi.org/10.1007/JHEP10(2015)191
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DOI: https://doi.org/10.1007/JHEP10(2015)191