Three approaches to the Howe duality between quantum general linear supergroups

2025/06/02 by Luo, Li, Yu, Xirui, Zhou, Zhongguo
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2506.01613

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(\mathfrakgl_m|n). Moreover, we show that these three approaches are equivalent by giving their action formulas explicitly.

Related

• Geometric Howe dualities of finite type
• Structure And Representations Of The Quantum General Linear Supergroup
• Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup
• Howe Duality for Quantum Queer Superalgebras
• Dual canonical bases for the quantum general linear supergroup