Classification of simple weight modules for the Neveu-Schwarz algebra with a finite-dimensional weight space

We show that the support of a simple weight module over the Neveu-Schwarz algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite-dimensional. As a corollary we obtain that every simple weight module over the Neveu-Schwarz algebra, having a non-trivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either a highest or lowest weight module, or else a module of the intermediate series). This result generalizes a theorem which was originally given on the Virasoro algebra.