Howe duality in the toroidal setting
Fulin Chen, Xin Huang, Shaobin Tan
TL;DR
This paper extends classical Howe duality to the toroidal setting by constructing dual pairs acting on oscillator modules of symplectic toroidal Lie algebras with irrational quantum tori.
Contribution
It introduces a new framework for Howe duality in the context of symplectic toroidal Lie algebras, expanding the classical theory to a more general setting.
Findings
Construction of dual pairs on oscillator modules
Extension of Howe duality to toroidal Lie algebras
Analysis of actions on modules in the toroidal setting
Abstract
In this paper, we construct and study various dual pairs acting on the oscillator modules of the symplectic toroidal Lie algebras coordinated by irrational quantum tori. This extends the classical Howe dual pairs to the toroidal setup.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra