with central chargeN |
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Authors: | Edward Frenkel Victor Kac Andrey Radul Weiqiang Wang |
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Institution: | (1) Department of Mathematics, Harvard University, 02138 Cambridge, MA, USA;(2) Department of Mathematics, MIT, 02139 Cambridge, MA, USA |
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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.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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