Tensor Product Weight Representations of the Neveu–Schwarz Algebra

Abstract

We study the tensor product of a highest weight module with an intermediate series module over the Neveu–Schwarz algebra. If the highest weight module is nontrivial, the weight spaces of such a tensor product are infinite dimensional. We show that such a tensor product is indecomposable. Using a “shifting technique” developed by H. Chen, X. Guo, and K. Zhao for the Virasoro algebra case, we give necessary and sufficient conditions for such a tensor product to be irreducible. Furthermore, we give necessary and sufficient conditions for two such tensor products to be isomorphic.

Key Words:

• Indecomposable module
• Irreducible module
• Isomorphism
• Neveu–Schwarz algebra
• Tensor product module

2010 Mathematics Subject Classification:

• 17B10
• 17B65
• 17B68

ACKNOWLEDGMENTS

The research was carried out during the visit of the author at Wilfrid Laurier University in 2013. The hospitality of Wilfrid Laurier University is gratefully acknowledged. The author would like to express his deep gratitude to Prof. Kaiming Zhao and Dr. Hongjia Chen for valuable discussions and their constant care.

Notes

Communicated by A. Elduque.