  Schubert varieties are irreducible subvarieties of homogeneous manifold,
which are important to understand the geometry of homogeneous manifold G/P and
the action of the semisimple Lie group G. Consider the space of effective
cycles in G/P with homology class equal to an integral multiple of the homology
class of a Schubert variety X_w of type w. We will show that for a smooth
Schubert variety X_w in Hermitian symmetric space with trivial exceptions, this
cycle space is simple: any irreducible subvariety X with homology class
[X]=r[X_w] is again a Schubert variety of type w.
