  We construct a U_h(sp(4))-equivariant quantization of the four-dimensional
complex sphere S^4 regarded as a conjugacy class, Sp(4)/Sp(2)x Sp(2), of a
simple complex group with non-Levi isotropy subgroup, through an operator
realization of the quantum polynomial algebra C_h[S^4] on a highest weight
module of U_h(sp(4)).
