  We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized
fractional quantum Hall states to be the exact and unique ground states.
Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the
generalized fractional quantum Hall states are extended objects. They are
vortex-like excitations with fractional charges $+(-)1/m^3$ in the total
configuration space CP$^3$. The density correlation function of the Zhang-Hu
states indicates that they are incompressible liquid.
