Vertex algebras, Kac-Moody algebras, and the Monster
- 1 May 1986
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 83 (10) , 3068-3071
- https://doi.org/10.1073/pnas.83.10.3068
Abstract
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A . 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.Keywords
This publication has 1 reference indexed in Scilit:
- A natural representation of the Fischer-Griess Monster with the modular function J as characterProceedings of the National Academy of Sciences, 1984