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.