A realisation of the quantum linear superalgebra

Abstract

We reconstruct the quantum enveloping superalgebra ${\bf U}(\mathfrak{gl}_{m|n})$ over $\mathbb Q(v)$ via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators of ${\bf U}(\mathfrak{gl}_{m|n})$ and explicit multiplication formulas between the generators and an arbitrary basis element.