Vertex operator representations of quantum affine superalgebras

TL;DR

This paper constructs vertex operator representations for quantum affine superalgebras associated with specific affine Kac-Moody superalgebras, classifies their finite-dimensional irreducible representations, and utilizes Drinfeld realization and quantum correspondences.

Contribution

It develops vertex operator constructions for level 1 representations and classifies finite-dimensional irreducible modules of these superalgebras, advancing understanding of their structure.

Findings

Constructed vertex operator representations for the superalgebras.

Classified finite-dimensional irreducible representations.

Utilized Drinfeld realization and quantum correspondences.

Abstract

Let Uq(g) be the quantum affine superalgebra associated with an affine Kac-Moody superalgebra g which belongs to the three series osp(1|2n)^(1),sl(1|2n)^(2) and osp(2|2n)^(2). We develop vertex operator constructions for the level 1 irreducible integrable highest weight representations and classify the finite dimensional irreducible representations of Uq(g). This makes essential use of the Drinfeld realisation for Uq(g), and quantum correspondences between affine Kac-Moody superalgebras, developed in earlier papers.