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.
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Communicated by M. Jimbo
Supported by a Junior Fellowship from Harvard Society of Fellows and in part by NSF grant DMS-9205303.
Supported in part by NSF grant DMS-9103792.
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Frenkel, E., Kac, V., Radul, A. et al. 
with central chargeN
.
Commun.Math. Phys. 170, 337–357 (1995). https://doi.org/10.1007/BF02108332
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DOI: https://doi.org/10.1007/BF02108332