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. https://resolver.caltech.edu/CaltechAUTHORS:20170408-165608354
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Abstract
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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Issue or Number: | 1 | |||||||||
DOI: | 10.1215/S0012-7094-92-06604-X | |||||||||
Record Number: | CaltechAUTHORS:20170408-165608354 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170408-165608354 | |||||||||
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. https://projecteuclid.org/euclid.dmj/1077294666 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 76283 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | 1Science Import | |||||||||
Deposited On: | 12 Mar 2018 21:01 | |||||||||
Last Modified: | 15 Nov 2021 16:58 |
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