Decomposition of modules over the Weyl algebra

Abstract: The thesis consists of two papers that treat decomposition of modules over the Weyl algebra. In the first paper decomposition of holonomic modules is used to prove that there is a finite set of Noetherian operators that suffice to distinguish the elements in a primary ideal. In the second the decomposition of the direct image of the root-to-coefficients mapping are constructed using the representation theory of the symmetric group, in particular higher Specht polynomials.