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- W2292883093 abstract "In this chapter we shall discuss standard (or integrable highest weight) representations of affine Kac-Moody algebras from the point of view of vertex operator algebra theory. This will also provide the setting for the next chapter. We restrict our attention to a simple Lie algebra G of type A, D or E. Let G be the corresponding affine Lie algebra and let l be a positive integer. We show that a certain distinguished one of the level l standard G-modules L(l,0) has the structure of a vertex operator algebra and that every level l standard G-module, at least every such module which can be obtained from the tensor product of l basic modules (i.e., level 1 standard modules for affine Lie algebras of type Â, D or E), is an irreducible module for this vertex operator algebra. Conversely, every irreducible module for the vertex operator algebra L(l, 0) is also a standard (G-module of level l. The Virasoro algebra for the vertex operator algebra L(l,0) comes from a canonical vertex operator associated with the (suitably normalized) Casimir operator for G. Using an abelian intertwining algebra (see Chapter 12) associated with the direct sum of l copies of the weight lattice, we also construct intertwining operators for irreducible L(l, 0)-modules. There is some overlap between the results in this chapter and those in [FZ], which uses a different approach, involving Verma modules." @default.
- W2292883093 created "2016-06-24" @default.
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- W2292883093 date "1993-01-01" @default.
- W2292883093 modified "2023-09-28" @default.
- W2292883093 title "Affine Lie algebras and vertex operator algebras" @default.
- W2292883093 doi "https://doi.org/10.1007/978-1-4612-0353-7_13" @default.
- W2292883093 hasPublicationYear "1993" @default.
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