A family of non-weight modules over the super-Virasoro algebras

Abstract In this paper, a family of non-weight modules over the super-Virasoro algebras are constructed. These modules over the Ramond algebra are free of rank 1 when restricted as modules over the Cartan subalgebra h , while these modules over the Neveu-Schwarz algebra are free of rank 2 when restricted as modules over the Cartan subalgebra H . We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free U ( h ) -modules of rank 1 over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free U ( H ) -modules of rank 2 over the super-Virasoro algebra of Neveu-Schwarz type.