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Representations of the moonshine module vertex operator algebra. (English) Zbl 0808.17013
Sally, Paul J. jun. (ed.) et al., Mathematical aspects of conformal and topological field theories and quantum groups. AMS-IMS-SIAM summer research conference, June 13-19, 1992, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 175, 27-36 (1994).
Summary: We consider the moonshine module vertex operator algebra constructed by Frenkel-Lepowsky-Meurman. This algebra has a unique irreducible module, the adjoint module, and any module is completely reducible. This proves the first part of the FLM’s conjecture on the moonshine module.
The detailed version of this paper will be submitted for publication elsewhere.
For the entire collection see [Zbl 0801.00049].

MSC:
17B65 Infinite-dimensional Lie (super)algebras
17B69 Vertex operators; vertex operator algebras and related structures
17B68 Virasoro and related algebras
20D08 Simple groups: sporadic groups
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