The tetrahexahedric angular Calogero model

Understand

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.