  We introduce a Hilbert $A$-module structure on the higher oscillatory module,
where $A$ denotes the $C^*$-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.
