Classification of simple quasifinite modules for contact superconformal algebras with $N\ne4$

TL;DR

This paper classifies all simple jet modules and quasifinite modules for contact superconformal algebras with N not equal to 4, confirming a conjecture for these cases.

Contribution

It provides a complete classification of simple modules for certain contact superconformal algebras, verifying a conjecture in the field.

Findings

Matínez-Zelmanov's conjecture holds for N ≠ 4

All simple jet modules are classified

All simple quasifinite modules are classified

Abstract

In this paper, we classify all simple jet modules for contact superconformal algebras $\mathcal{K}(N;\epsilon)$ with $N\neq4$. Then all simple quasifinite modules for $\widehat{\mathcal{K}}(N;\epsilon)$ ($N\neq4$), the universal central extension of $\mathcal{K}(N;\epsilon)$, are classified. Our results show that Mat\'{i}nez-Zelmanov's conjecture in \cite{MZe1} holds for $\mathcal{K}(N;\epsilon)$ ($N\ne4$).