Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact subalgebra

TL;DR

This paper classifies all simple modules for the Neveu-Schwarz algebra and its contact subalgebra, providing a comprehensive understanding of their structure and representation theory.

Contribution

It offers the first complete classification of simple Harish-Chandra modules over these superalgebras, extending previous partial results.

Findings

Complete classification of simple jet modules for the Neveu-Schwarz algebra

Classification of simple Harish-Chandra modules for the algebra and subalgebra

New insights into the structure of modules over superalgebras

Abstract

In this paper, we classify all simple jet modules for the Neveu-Schwarz algebra $\widehat{\mathfrak{k}}$ and its contact subalgebra $\mathfrak{k}^+$. Based on these results, we give a classification of simple Harish-Chandra modules for $\widehat{\mathfrak{k}}$ and $\mathfrak{k}^+$.