Annales Henri Poincaré

, Volume 15, Issue 2, pp 313–344 | Cite as

Symmetries of Quantum Lax Equations for the Painlevé Equations

  • Hajime NagoyaEmail author
  • Yasuhiko Yamada


Based on the fact that the Painlevé equations can be written as Hamiltonian systems with affine Weyl group symmetries, a canonical quantization of the Painlevé equations preserving such symmetries has been studied recently. On the other hand, since the Painlevé equations can also be described as isomonodromic deformations of certain second-order linear differential equations, a quantization of such Lax formalism is also a natural problem. In this paper, we introduce a canonical quantization of Lax equations for the Painlevé equations and study their symmetries. We also show that our quantum Lax equations are derived from Virasoro conformal field theory.


Automorphism Group Commutation Relation Weyl Group Dynkin Diagram Gauge Factor 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsKobe UniversityKobeJapan

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