Three approaches to the Howe duality between quantum general linear supergroups

Abstract

The Howe duality between quantum general linear supergroups was firstly established by Y. Zhang via quantum coordinate superalgebras. In this paper, we provide two other approaches to this Howe duality. One is constructed by quantum differential operators, while the other is based on the Beilinson-Lusztig-MacPherson realization of $U_q({\mathfrak{gl}}_{m|n})$. Moreover, we show that these three approaches are equivalent by giving their action formulas explicitly.

22 pages