Irreducible modules for super-Virasoro algebras from algebraic D-modules

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(h)-free modules. Additionally, we provide several families of new irreducible super-Virasoro modules via our constructed functors.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, a new family of functors from the module category of the Weyl algebra to the module category of the super-Virasoro algebras is introduced. The properties of these functors, including irreducibility preservation and natural isomorphisms, are investigated. Using these functors, old irreducible super-Virasoro modules, including those from the irreducible intermediate series and irreducible U(h)-free modules, are recovered. Additionally, several families of new irreducible super-Virasoro modules are provided via the constructed functors.