# Irreducible weight modules with a finite-dimensional weight space over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra

## TL;DR

This paper proves that all irreducible weight modules with finite-dimensional weight spaces over the twisted N=1 Schrödinger-Neveu-Schwarz algebra are Harish-Chandra modules, showing a classification result in representation theory.

## Contribution

It establishes that no simple mixed modules exist over this algebra, confirming all such modules are Harish-Chandra modules, thus advancing understanding of its representation structure.

## Key findings

- No simple mixed modules over the algebra
- All irreducible weight modules with finite-dimensional weight spaces are Harish-Chandra modules
- Provides a classification of modules over the twisted N=1 Schrödinger-Neveu-Schwarz algebra

## Abstract

It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra module.