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arXiv · 2001.00701

Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras

Robert McRae
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Abstract

We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When $\mathfrak{g}=\mathfrak{sl}_2$, these results extend previous joint work with J. Yang, but the method used here is different. Here, we construct intertwining operators by solving Knizhnik-Zamolodchikov equations for three-point correlation functions associated to $\hat{\mathfrak{g}}$, and we identify obstructions to the construction arising from the possible non-existence of series solutions having a prescribed form.

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Robert McRae. 2020-01-03. Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras. https://doi.org/10.1016/j.aim.2020.107351

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