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Letters in Mathematical Physics

, Volume 104, Issue 11, pp 1407–1423 | Cite as

Quantum Torus Symmetry of the KP, KdV and BKP Hierarchies

  • Chuanzhong Li
  • Jingsong He
Article

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 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.

Keywords

KP hierarchy quantum torus symmetry quantum torus constraint KdV hierarchy BKP hierarchy 

Mathematics Subject Classification

37K05 37K10 37K40 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsNingbo UniversityNingboPeople’s Republic of China

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