Quantum Torus Symmetry of the KP, KdV and BKP Hierarchies
Quantum Torus Symmetry of the KP, KdV and BKP Hierarchies
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DOI：
10.1007/s11005-014-0716-z
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发表时间：
2013-12
影响因子：
1.2
通讯作者：
Chuanzhong Li;Jingsong He
中科院分区：
文献类型：
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作者：
Chuanzhong Li;Jingsong He
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 theW∞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 further derive the quantum torus constraints on their tau functions. These quantum torus constraints might have applications in the quantum field theory, supersymmetric gauge theory and so on.
