Algebraic description of D-modules associated to 3×3 matrices

AbstractIn this paper we give a classification of regular holonomic D-modules whose characteristic variety is contained in the union of the conormal bundles to the orbits of the group of invertible matrices of order 3. The main result is an equivalence between the category of these differential modules and the one of graded modules of finite type over the Weyl algebra of invariant differential operators under the action of the group of invertible matrices. We infer that such objects can be understood in terms of finite diagrams of complex vector spaces of finite dimension related by linear maps