  We study irreducible *-representations of a certain quantization of the
algebra of polynomial functions on a generalized flag manifold regarded as a
real manifold. All irreducible *-representations are classified for a subclass
of flag manifolds containing in particular the irreducible compact Hermitian
symmetric spaces. For this subclass it is shown that the irreducible
*-representations are parametrized by the symplectic leaves of the underlying
Poisson bracket. We also discuss the relation between the quantized flag
manifolds studied in this paper and the quantum flag manifolds studied by
Soibelman, Lakshimibai and Reshetikhin, Jurco and Stovicek, and Korogodsky.
