Cohomology of the de Rham complex twisted by the oscillatory representation

Abstract

We introduce a Hilbert $A$-module structure on the higher oscillatory module, where $A$ denotes the $C^{\ast }$-algebra of bounded endomorphisms of the basic oscillatory module. We also define the notion of an exterior covariant derivative in an $A$-Hilbert bundle and use it for a construction of an $A$-elliptic complex of differential operators for certain symplectic manifolds equipped with a symplectic connection.

10 pages, submitted to Differential Geometry and its Applications

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