Integrable modules over affine Lie superalgebras sl(1|n)^

TL;DR

This paper classifies integrable modules over the affine Lie superalgebra sl(1|n)^ with positive central charge, establishing a complete correspondence between irreducible modules and simple vertex algebra representations.

Contribution

It provides a comprehensive description of integrable modules over sl(1|n)^ and links them to simple vertex algebra representations, a novel classification in this context.

Findings

Irreducible modules form a complete set for the simple vertex algebra.

The category of integrable modules with positive central charge is fully described.

A correspondence between modules and vertex algebra representations is established.

Abstract

We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.