Dyon-oscillator duality. Hidden symmetry of the Yang-Coulomb monopole

In this report, in the framework of Lilt analytical approach and with help of a generalized version of the Hurwitz transformation, the five-dimensional bound system composed of the Yang monopole coupled to a particle with all SU(2) isospin and a Coulomb interaction. is constructed from the eight-dimensional quantum oscillator. The generalized Runge-Lenz vector and the SO(G) group of the hidden symmetry are established. It is also shown that group of hidden symmetry makes it possible to calculate the spectrum of the system by a purely algebraic method.