Noncommutative vector bundles over fuzzy CPN and their covariant derivatives

We generalise the construction of fuzzy CPN in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommutative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space