New simple Virasoro modules from Weyl algebra modules

In this paper, we construct a class of modules N(P, V) over the Virasoro algebra from modules P over the degree-1 Weyl algebra K and modules V over the positive part of the Virasoro algebra. This generalizes a construction in [22] and provides a unified description of many known examples of Virasoro modules, for example, in [24,22,3,23]. We obtain the necessary and sufficient conditions for N(P, V) to be simple and also determine the isomorphism class of these modules. At the end of the paper, we compare the modules N(P, V) with other known simple Virasoro modules, concluding that they are new simple modules in general. (C) 2022 Elsevier Inc. All rights reserved.