Quantum Torus symmetry of the KP, KdV and BKP hierarchies

Abstract

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 $W_{\infty }$ 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.

published in Lett. Math. Phys. online ahead of print 15 August 2014

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Cited by in corpus (8)

• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Supersymmetric BKP systems and their symmetries
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Sato theory on the $q$-Toda hierarchy and its extension
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy