Classification of Simple Weight Modules for the Neveu–Schwarz Algebra with a Finite-Dimensional Weight Space

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 nontrivial 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 nontrivial 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.

Key Words:

• Harish–Chandra module
• Neveu–Schwarz algebra
• Weight module

2000 Mathematics Subject Classification:

• 17B10
• 17B65
• 17B68

Acknowledgments

Supported by the National Natural Science Foundation of China (No. 10931006).

Notes

Communicated by A. Elduque.