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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
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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