Multiparameter Twisted Weyl Algebras

TL;DR

This paper introduces multiparameter twisted Weyl algebras, a new family of algebras that generalize existing structures, classifies their simple modules, and describes Whittaker pairs within this framework.

Contribution

It defines a new class of twisted generalized Weyl algebras, parametrizes their simple quotients, and extends classification results for modules and Whittaker pairs.

Findings

Unified framework for various Weyl algebra generalizations

Complete classification of simple weight modules

Description of Whittaker pairs up to isomorphism

Abstract

We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras.