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Vertex operator algebras associated to representations of affine and Virasoro algebras

Frenkel, Igor B. and Zhu, Yongchang (1992) Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Mathematical Journal, 66 (1). pp. 123-168. ISSN 0012-7094. doi:10.1215/S0012-7094-92-06604-X.

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The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formula for affine roots systems discovered earlier by Macdonald [M]. Though the Macdonald identity found its natural context in representation theory, its mysterious modular invariance was not understood until the work of Witten [W-I on the geometric realization of representations of the loop groups corresponding to loop algebras. The work of Witten clearly indicated that the representations of loop groups possess a very rich structure of conformal field theory which appeared in physics literature in the work of Belavin, Polyakov, and Zamolodchikov [BPZ-I. Independently (though two years later), Borcherds, in an attempt to find a conceptual understanding of a certain algebra of vertex operators invariant under the Monster [FLM1], introduced in [B-I a new algebraic structure. We call vertex operator algebras a slightly modified version of Borcherd’s new algebras [FLM2].

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Additional Information:© 1992 Duke University Press. Received 14 August 1991. Revision received 5 October 1991. We would like to thank G. Zuckerman for stimulating discussions and F. Akman for reading the manuscript. I. F. acknowledges the support from NSF Grant DMS-8906772 and the Guggenheim Memorial Foundation. Y. Z. is grateful to the mathematics department of Yal University wher part of this work was done and for the support from a Caltech Division Research Fellowship.
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Official Citation:Frenkel, Igor B.; Zhu, Yongchang. Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Math. J. 66 (1992), no. 1, 123--168. doi:10.1215/S0012-7094-92-06604-X.
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Deposited On:12 Mar 2018 21:01
Last Modified:15 Nov 2021 16:58

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