Irreducible Modules for Super-Virasoro Algebras from Algebraic D-Modules

TL;DR

This paper introduces a novel method using algebraic D-modules to construct and analyze irreducible modules for super-Virasoro algebras, recovering known modules and discovering new ones.

Contribution

It presents a new family of functors from Weyl algebra modules to super-Virasoro modules, enabling the construction of both known and new irreducible modules.

Findings

Recovered classical irreducible super-Virasoro modules

Constructed new families of irreducible modules

Established properties of the functors, including irreducibility preservation

Abstract

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on irreducibility preservation and natural isomorphisms. By utilizing these functors, we recover some old irreducible super-Virasoro modules, including those from the irreducible intermediate series as well as irreducible $U(\mathfrak{h})$-free modules. Additionally, we provide several families of new irreducible super-Virasoro modules via our constructed functors.