Abstrakt
For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of Kostant's symplectic spinor bundle. Defining a Hilbert C-*-structure on this bundle for a suitable C-*-algebra, we obtain an elliptic C-*-complex in the sense of Mishchenko-Fomenko.
Its cohomology groups appear to be finitely generated projective Hilbert C-*-modules. The paper can serve as a guide for handling differential complexes and PDEs on Hilbert bundles.