What question did this study set out to answer?

This research aims to explore and establish equivalences among three approaches to Howe duality in quantum general linear supergroups.

July 10, 2026Open Access

Three approaches to the Howe duality between quantum general linear supergroups

LLLi‐Shi LuoNorfolk State University XYXiaolan YuHangzhou Normal University ZZZhongguo ZhouHohai University

Key Points

This research aims to explore and establish equivalences among three approaches to Howe duality in quantum general linear supergroups.
Utilizes quantum differential operators to construct an approach to Howe duality.
Applies the Beilinson-Lusztig-MacPherson realization of Uq(glm|n) in another approach.
Compares the three methods by providing explicit action formulas.
Demonstrated equivalence of the three approaches to Howe duality in quantum supergroups.
Presented explicit action formulas that support the equivalence of different methods.

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 additional approaches to this Howe duality. One is constructed by quantum differential operators, while the other is based on the Beilinson-Lusztig-MacPherson realization of Uq(glm|n). Moreover, we show that these three approaches are equivalent by giving their action formulas explicitly.

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