On Cohen--Macaulay modules over the Weyl algebra

TL;DR

This paper introduces a new definition of Cohen--Macaulay modules over the Weyl algebra and provides conditions under which certain hypergeometric modules satisfy this property.

Contribution

It offers the first definition of Cohen--Macaulay modules in the context of the Weyl algebra and identifies criteria for hypergeometric modules to be Cohen--Macaulay.

Findings

Defined Cohen--Macaulay modules over the Weyl algebra

Provided sufficient conditions for GKZ hypergeometric modules to be Cohen--Macaulay

Enhanced understanding of module properties in algebraic analysis

Abstract

We propose a definition of Cohen--Macaulay modules over the Weyl algebra $D$ and give a sufficient condition for a GKZ $A$-hypergeometric $D$-module to be Cohen--Macaulay.