Drinfeld realisations and vertex operator representations of quantum affine superalgebras

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.

This paper combines and supersedes two prior papers arXiv:1611.06449 and arXiv:1707.09140