Duflo Theorem for a Class of Generalized Weyl Algebras

TL;DR

This paper extends the Duflo theorem to a specific class of generalized Weyl algebras, showing that simple modules' annihilators are linked to highest weight modules, thus deepening understanding of their structure.

Contribution

It introduces a Duflo theorem for a particular class of generalized Weyl algebras, connecting simple modules to highest weight modules.

Findings

Proves the Duflo theorem for the specified class of generalized Weyl algebras.

Shows that annihilators of simple modules correspond to those of highest weight modules.

Enhances the structural understanding of modules over these algebras.

Abstract

For a special class of generalized Weyl algebras, we prove a Duflo theorem stating that the annihilator of any simple module is in fact the annihilator of a simple highest weight module.