A paper claims a generalized Kustaanheimo-Stiefel duality between N=2n singular oscillators and (n+1)-dimensional generalized MICZ-Kepler systems, with exact solutions and hidden symmetry algebras, but the required transformation only provably exists for special n.
Dyon-Oscillator Duality. Hidden Symmetry of the Yang-Coulomb Monopole
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abstract
In this article, in the framework of an analytical approach and with help of the generalized version of the Hurwitz transformation the five--dimensional bound system composed of the Yang monople coupled to a particle of the isospin by SU(2) and Coulomb interaction is constructed from the eight-dimensional quantum oscillator. The generalized Runge-Lentz vector and the SO(6) group of the hidden symmetry are established. It is also shown that group of hidden symmetry makes it possible to calculate the spectrum of system by a pure algebraic method.
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Generalized KS transformations, $ND$ singular oscillator and generalized MICZ-Kepler system
A paper claims a generalized Kustaanheimo-Stiefel duality between N=2n singular oscillators and (n+1)-dimensional generalized MICZ-Kepler systems, with exact solutions and hidden symmetry algebras, but the required transformation only provably exists for special n.