Abstract
We shall present the notion of relative untwisted vertex operators, following our announcement [DL1]. We begin with some well-known structure (see e.g. [FLM3]), which we “relativize” to h * . Using the affinization of the abelian Lie algebra h together with the related Heisenberg algebra ĥ z and the irreducible module M(1), we construct the untwisted space V L and the action of certain operators on it. The vacuum space Ω* for the Heisenberg algebra (ĥ * ) z associated with h * plays a fundamental role. We define the relative vertex operators Y*(a,z) and more generally, Y*(v,z), using h * systematically to modify the definition of the usual (unrelativized) vertex operators. Elementary properties of the operators are discussed. For the (important) degenerate case h * = 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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© 1993 Springer Science+Business Media New York
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Dong, C., Lepowsky, J. (1993). Relative untwisted vertex operators. In: Generalized Vertex Algebras and Relative Vertex Operators. Progress in Mathematics, vol 112. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0353-7_3
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DOI: https://doi.org/10.1007/978-1-4612-0353-7_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6721-8
Online ISBN: 978-1-4612-0353-7
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