Tensor product weight representations of the Neveu-Schwarz algebra

Abstract

In this paper, the tensor product of highest weight modules with intermediate series modules over the Neveu-Schwarz algebra is studied. The weight spaces of such tensor products are all infinitely dimensional if the highest weight module is nontrivial. We find that all such tensor products are indecomposable. We give the necessary and sufficient conditions for these tensor product modules to be irreducible by using shifting technique established for the Virasoro case in [13]. The necessary and sufficient conditions for any two such tensor products to be isomorphic are also determined.