Classification of simple modules with finite-dimensional weight spaces for the N = 2 Ramond algebra

TL;DR

This paper classifies all simple weight modules with finite-dimensional weight spaces over the N=2 Ramond algebra, identifying them as highest weight, lowest weight, or certain cuspidal modules.

Contribution

It provides a complete classification of simple modules with finite-dimensional weight spaces over the N=2 Ramond algebra, including new insights into cuspidal modules.

Findings

Modules are either highest weight, lowest weight, or cuspidal with bounded weight multiplicities.

All such modules are explicitly characterized.

The classification completes the understanding of simple weight modules over this algebra.

Abstract

In this paper, we classify all simple weight modules with finite-dimensional weight spaces over the $N=2$ Ramond algebra. Any such module $V$ is either a simple highest weight module or a simple lowest weight module, or a simple cuspidal module with ${\rm b}(V)\le 2$.