Drinfeld realisations and vertex operator representations of quantum affine superalgebras

Abstract

Drinfeld realisations are constructed for the quantum affine superalgebras of the series $\mathfrak{osp}(1|2n{)}^{(1)}$,$\mathfrak{sl}(1|2n{)}^{(2)}$ and $\mathfrak{osp}(2|2n{)}^{(2)}$. 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