Nonlinear symmetry algebra of the MIC-Kepler problem on the sphere S3

The quantum mechanical problem of motion in the dual charged Coulomb field modified by a centrifugal term (MIC-Kepler problem) is considered in the three-dimensional space of constant positive curvature S-3. Conserved operators in this problem form a cubic algebra similar to that of the Kepler problem on S-3. The explicit form of invariants of this algebra shows that its representation associated with the MIC-Kepler problem on S-3 is a nondegenerate one. The cubic symmetry algebra is used to obtain the energy spectrum of the problem.