Communications in Mathematical Physics

, Volume 172, Issue 2, pp 377–400 | Cite as

Character and determinant formulae of quasifinite representation of theW1+∞ algebra

  • H. Awata
  • M. Fukuma
  • Y. Matsuo
  • S. Odake


We diagonalize the Hilbert space of some subclass of the quasifinite module of theW1+∞ algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.


Neural Network Statistical Physic Hilbert Space Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. Awata
    • 1
  • M. Fukuma
    • 2
  • Y. Matsuo
    • 3
  • S. Odake
    • 4
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  3. 3.Uji Research Center, Yukawa Institute for Theoretical PhysicsKyoto UniversityUjiJapan
  4. 4.Department of Physics, Faculty of Liberal ArtsShinshu UniversityMatsumotoJapan

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