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

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.

arXiv comment18 pages; expanded Introduction and more examples added to Section 5 in this version

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Cited by in corpus (3)

• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge
• The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$
• The non-semisimple Kazhdan-Lusztig category for affine ${\mathfrak{sl}}_2$ at admissible levels