Vertex operator algebras associated to representations of affine and Virasoro algebras
- Creators
- Frenkel, Igor B.
- Zhu, Yongchang
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].
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.Additional details
- Eprint ID
- 76283
- DOI
- 10.1215/S0012-7094-92-06604-X
- Resolver ID
- CaltechAUTHORS:20170408-165608354
- DMS-8906772
- NSF
- John Simon Guggenheim Foundation
- Caltech Division of Physics, Mathematics and Astronomy
- Created
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2018-03-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field