标题： 量子广义线性超群之间Howe对偶的三种方法 显示英文标题

标题： Three approaches to the Howe duality between quantum general linear supergroups

摘要： 量子一般线性超群之间的Howe对偶性最初由张毅通过量子坐标超代数建立。本文提供了这种Howe对偶性的另外两种方法：一种是通过量子微分算子构造的，另一种基于Beilinson-Lusztig-MacPherson对$U_q(\mathfrak{gl}_{m|n})$的实现。此外，我们通过明确给出它们的作用公式来证明这三种方法是等价的。 显示英文摘要

摘要： 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.