English

Three approaches to the Howe duality between quantum general linear supergroups

Quantum Algebra 2026-05-07 v2 Representation Theory

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 Uq(glmn)U_q(\mathfrak{gl}_{m|n}). Moreover, we show that these three approaches are equivalent by giving their action formulas explicitly.

Keywords

Cite

@article{arxiv.2506.01613,
  title  = {Three approaches to the Howe duality between quantum general linear supergroups},
  author = {Li Luo and Xirui Yu and Zhongguo Zhou},
  journal= {arXiv preprint arXiv:2506.01613},
  year   = {2026}
}

Comments

22 pages

R2 v1 2026-07-01T02:54:20.861Z