  We consider a superintegrable quantum potential in two-dimensional Euclidean
space with a second and a third order integral of motion. The potential is
written in terms of the fourth Painleve transcendent. We construct for this
system a cubic algebra of integrals of motion. The algebra is realized in terms
of parafermionic operators and we present Fock type representations which yield
the corresponding energy spectra. We also discuss this potential from the point
of view of higher order supersymmetric quantum mechanics and obtain ground
state wave functions.
