Hurwitz transformation and oscillator representation of a 5D “isospin” particle

The correspondence between 5D quantized Kepler problem and 8D harmonic oscillator in the case of topologically nontrivial constraints imposed on the wavefunction of the latter is considered. It is shown that both the “isospinor” and the “isovector” particles on the SU(2) instanton plus 1R background in 5D can be described in terms of an 8D singular oscillator.