Representations of affine Lie superalgebras and their quantization in type A

TL;DR

This paper introduces a new family of irreducible modules for affine Lie superalgebras and their quantum deformations, expanding the understanding of their representation theory.

Contribution

It constructs irreducible modules induced from Heisenberg subalgebras and develops their quantum deformations specifically for type A affine superalgebras.

Findings

New irreducible modules over affine Lie superalgebras

Quantum deformations of these modules for type A

Enhanced understanding of superalgebra representations

Abstract

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the quantum affine superalgebra of type A.