  This article deals with nonrelativistic study of a D-dimensional
superintegrable system, which generalizes the ordinary isotropic oscillator
system. The coefficients for the expansion between the hyperspherical and
Cartesian bases (transition matrix), and vice-versa, are found in terms of the
SU(2) Clebsch--Gordan coefficients analytically continued to real values of
their arguments. The diagram method, which allow one to construct a transition
matrix for arbitrary dimension, is developed.
