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

TL;DR

This paper classifies simple weight modules over the Neveu-Schwarz algebra, showing their support covers the entire weight lattice and characterizing modules with finite-dimensional weight spaces as Harish-Chandra modules, extending Virasoro algebra results.

Contribution

It generalizes the classification of simple weight modules to the Neveu-Schwarz algebra, identifying conditions for finite-dimensional weight spaces and their structure.

Findings

Support of modules with infinite-dimensional weight spaces is the entire weight lattice.

Modules with finite-dimensional weight spaces are Harish-Chandra modules.

Extension of Virasoro algebra classification to Neveu-Schwarz algebra.

Abstract

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.