Admissible modules over affine Lie superalgebras: The final step in the characterization

TL;DR

This paper completes the characterization of simple admissible modules over affine Lie superalgebras, focusing on zero-level modules, a key challenge in the field.

Contribution

It provides the final step in classifying simple admissible modules over affine Lie superalgebras, especially addressing the zero-level case.

Findings

Complete classification of simple admissible modules

Resolution of zero-level module characterization

Advancement in understanding affine Lie superalgebra representations

Abstract

Over the past three decades, there have been several attempts to characterize modules over affine Lie superalgebras. One of the main issues in this regard is dealing with zero-level modules. In this paper, we study these modules and {complete the characterization} of simple admissible modules over affine Lie superalgebras.