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

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.