  In this manuscript we make a general study of the representations realized,
for a reductive Lie group of Harish-Chandra class, on the compactly supported
sheaf cohomology groups of an irreducible finite-rank polarized homogeneous
vector bundle defined in a generalized complex flag space. In particular, we
show that the representations obtained are minimal globalizations of
Harish-Chandra modules and that there exists a whole number q, depending only
on the orbit, such that all cohomologies vanish in degree less than q. The
representation realized on the q-th cohomology group is called a standard
analytic module. Our main result is a geometric proof that a standard analytic
module embeds naturally in an associated standard module defined on the full
flag space of Borel subalgebras. As an application, we give geometric
realizations for irreducible submodules of some principal series
representations in case the group is complex.
