On Involutive Homogeneous Varieties and Representations of Weyl Algebras

This paper is concerned with the geometry of minimal involutive homogeneous varieties in complex affine 2n-space and its application to the study of the representation theory of the nth complex Weyl algebra An. The main results are the existence of minimal involutive homogeneous varieties of any given codimension, and of An-modules that have these varieties for characteristic variety. We also determine conditions on the codimensions of An-modules M and N under which Ext1(M, N) is a finite dimensional vector space.