Communications in Mathematical Physics

, Volume 170, Issue 2, pp 337–357 | Cite as

Open image in new window with central chargeN

  • Edward Frenkel
  • Victor Kac
  • Andrey Radul
  • Weiqiang Wang


We study representations of the central extension of the Lie algebra of differential operators on the circle, the
algebra. We obtain complete and specialized character formulas for a large class of representations, which we call primitive; these include all quasi-finite irreducible unitary representations. We show that any primitive representation with central chargeN has a canonical structure of an irreducible representation of the
with the same central charge and that all irreducible representations of
with central chargeN arise in this way. We also establish a duality between “integral” modules of
and finite-dimensional irreducible modules ofgl N , and conjecture their fusion rules.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Differential Operator 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Edward Frenkel
    • 1
  • Victor Kac
    • 2
  • Andrey Radul
    • 2
  • Weiqiang Wang
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsMITCambridgeUSA

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