Classification of simple quasifinite modules for contact superconformal algebras with $N\ne 4$

Abstract

In this paper, we classify all simple jet modules for contact superconformal algebras $\mathcal{K}(N;\hat{I}\mu )$ with $N\ne 4$. Then all simple quasifinite modules for $\hat{\mathcal{K}}(N;\hat{I}\mu )$ ($N\ne 4$), the universal central extension of $\mathcal{K}(N;\hat{I}\mu )$, are classified. Our results show that Matínez-Zelmanov's conjecture in \cite{MZe1} holds for $\mathcal{K}(N;\hat{I}\mu )$ ($N\ne 4$).