Simple Restricted modules for $N=2$ Neveu-Schwarz algebra

Abstract

In this paper, we first construct many simple restricted modules for the $N=2$ Neveu-Schwarz algebra $\mathcal{L}$. These modules contain the highest weight modules and Whittaker modules. Then we precisely characterize the simple restricted modules over $\mathcal{L}$ under certain conditions, and establish several equivalent conditions for a simple \(\mathcal{L}\)-module to be restricted. Finally, we prove that if one specific positive root element of $\mathcal{L}$ acts locally finitely on a simple $\mathcal{L}$-module $V$, then $V$ must be restricted.