A realisation of the quantum linear superalgebra

TL;DR

This paper reconstructs the quantum superalgebra for gl_{m|n} using quantum Schur superalgebras, providing a new basis and explicit multiplication formulas, advancing the algebraic understanding of quantum superalgebras.

Contribution

It introduces a novel basis for the quantum superalgebra and explicit multiplication formulas, enhancing the algebraic framework for quantum superalgebras.

Findings

New basis containing standard generators

Explicit multiplication formulas

Reconstruction of quantum 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.