Drinfeld realisations and vertex operator representations of quantum affine superalgebras

TL;DR

This paper constructs Drinfeld realizations for specific quantum affine superalgebras, develops vertex operator representations, and classifies their finite-dimensional irreducible representations, advancing the understanding of their structure and representations.

Contribution

It introduces explicit Drinfeld realizations for certain quantum affine superalgebras and classifies their finite-dimensional irreducible representations.

Findings

Drinfeld realizations constructed for three classes of quantum affine superalgebras.

Vertex operator representations developed for these superalgebras.

Finite-dimensional irreducible representations classified.

Abstract

Drinfeld realisations are constructed for the quantum affine superalgebras of the series ${\rm\mathfrak{osp}}(1|2n)^{(1)}$,${\rm\mathfrak{sl}}(1|2n)^{(2)}$ and ${\rm\mathfrak{osp}}(2|2n)^{(2)}$. By using the realisations, we develop vertex operator representations and classify the finite dimensional irreducible representations for these quantum affine superalgebras.