  It is known that all the vector bundles of the title can be obtained by
holomorphic induction from representations of a certain parabolic Lie algebra
on finite dimensional inner product spaces. The representations, and the
induced bundles, have composition series with irreducible factors. Our first
main result is the construction of an explicit differential operator
intertwining the bundle with the direct sum of its factors. Next, we study
Hilbert spaces of sections of these bundles. We use this to get, in particular,
a full description and a similarity theorem for homogeneous $n$-tuples of
operators in the Cowen-Douglas class of the Euclidean unit ball in $\mathbb
C^n$.
