Quantum Torus Symmetry of the KP, KdV and BKP Hierarchies

@article{Li2013QuantumTS,
  title={Quantum Torus Symmetry of the KP, KdV and BKP Hierarchies},
  author={Chuanzhong Li and Jingsong He},
  journal={Letters in Mathematical Physics},
  year={2013},
  volume={104},
  pages={1407-1423}
}
In this paper, we construct the quantum torus symmetry of the KP hierarchy and further derive the quantum torus constraint on the tau function of the KP hierarchy. That means we give a nice representation of the quantum torus Lie algebra in the KP system by acting on its tau function. Comparing to the W∞ symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Further by reduction, we also construct the quantum torus symmetries of the KdV and BKP hierarchies and… 

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