Inventiones mathematicae

, Volume 120, Issue 1, pp 379–408 | Cite as

Kac-Moody groups and integrability of soliton equations

  • Boris Feigin
  • Edward Frenkel


A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicity identified with infinitesimal action of the principal abelian subalgebra of the corresponding affine Kac-Moody algebra on a homogeneous space.


Soliton Field Theory Homogeneous Space Soliton Equation Abelian Subalgebra 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Boris Feigin
    • 1
    • 2
  • Edward Frenkel
    • 3
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.R.I.M.S.Kyoto UniversityKyotoJapan
  3. 3.Department of MathematicsHarvard UniversityCambridgeUSA

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