Simple restricted modules for Neveu-Schwarz algebra

TL;DR

This paper constructs and classifies simple restricted modules for the Neveu-Schwarz algebra, extending known modules and establishing a correspondence with modules of associated finite-dimensional solvable Lie superalgebras.

Contribution

It introduces a new construction of simple modules for the Neveu-Schwarz algebra, generalizing highest weight and Whittaker modules, and classifies simple modules for related superalgebras.

Findings

Established a 1-1 correspondence between simple modules and modules of solvable Lie superalgebras.

Constructed a broad class of simple modules generalizing existing types.

Classified all simple modules for two associated superalgebras.

Abstract

In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.