  The Lie algebra of vector fields on $R^m$ acts naturally on the spaces of
differential operators between tensor field modules. Its projective subalgebra
is isomorphic to $sl_{m+1}$, and its affine subalgebra is a maximal parabolic
subalgebra of the projective subalgebra with Levi factor $gl_m$. We prove two
results. First, we realize all injective objects of the parabolic category
O$^{gl_m}(sl_{m+1})$ of $gl_m$-finite $sl_{m+1}$-modules as submodules of
differential operator modules. Second, we study projective quantizations of
differential operator modules, i.e., $sl_{m+1}$-invariant splittings of their
order filtrations. In the case of modules of differential operators from a
tensor density module to an arbitrary tensor field module, we determine when
there exists a unique projective quantization, when there exists no projective
quantization, and when there exist multiple projective quantizations.
