  It is known that all the vector bundles of the title can be obtained by
holomorphic induction from representations of a certain parabolic group on
finite dimensional inner product spaces. The representations, and the induced
bundles, have composition series with irreducible factors. We give a condition
under which the bundle and the direct sum of its irreducible constituents are
intertwined by an equivariant constant coefficient differential operator. We
show that in the case of the unit ball in $\mathbb C^2$ this condition is
always satisfied. As an application we show that all homogeneous pairs of
Cowen-Douglas operators are similar to direct sums of certain basic pairs.
