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- Richard E. Borcherds
- Trinity College, Cambridge CB2 1TQ, England
抄録
<jats:p> It is known that the adjoint representation of any Kac-Moody algebra <jats:italic>A</jats:italic> can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of <jats:italic>A</jats:italic> . I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The “Moonshine” representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation. </jats:p>
収録刊行物
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- Proceedings of the National Academy of Sciences
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Proceedings of the National Academy of Sciences 83 (10), 3068-3071, 1986-05
Proceedings of the National Academy of Sciences
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詳細情報 詳細情報について
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- CRID
- 1363951793598246912
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- NII論文ID
- 30016279077
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- ISSN
- 10916490
- 00278424
- http://id.crossref.org/issn/00278424
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- データソース種別
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