Titlebook: Generalized Vertex Algebras and Relative Vertex Operators; Chongying Dong,James Lepowsky Book 1993 Springer Science+Business Media New Yor

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A Jacobi identity for relative untwisted vertex operators,eralizes the Jacobi identity in [FLM3] (Theorems 8.8.9 and 8.8.23) by removing all integrality restrictions on the “inner products” of lattice elements. Since the proof is very similar to that of Theorem 8.6.1 of [FLM3], we shall omit some computations, referring the reader to that proof for more details.

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Intertwining operators,eory (see for example [FHL]), it is natural to consider “intertwining operators” parametrized by the vectors in a module, mapping one module to another. In this chapter, we discuss duality for intertwining operators associated with module elements against vertex operators associated with algebra elements.

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fy the definition of the usual (unrelativized) vertex operators. Elementary properties of the operators are discussed. For the (important) degenerate case . = 0, some of the notation simplifies, and the material in this chapter amounts to a review of the corresponding basic structure explained in [FLM3].

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