On fusion rules and intertwining operators for the Weyl vertex algebra

Abstract

In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra. This way we confirm the conjecture on fusion rules based on the Verlinde algebra. We explicitly construct intertwining operators appearing in the formula for fusion rules. We present a result which relates irreducible weight modules for the Weyl vertex algebra to the irreducible modules for the affine Lie superalgebra $\widehat{gl(1|1)}$.

21 pages

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Cited by in corpus (16)

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• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Modularity of Bershadsky-Polyakov minimal models
• 3d Mirror Symmetry and the $\beta \gamma$ VOA
• Rigid tensor structure on big module categories for some $W$-(super)algebras in type $A$
• On the semisimplicity of the category $K{L}_k$ for affine Lie superalgebras
• Vertex algebraic intertwining operators among generalized Verma modules for affine Lie algebras
• On rationality of $\mathbb{C}$-graded vertex algebras and applications to Weyl vertex algebras under conformal flow
• Representations of the Nappi--Witten vertex operator algebra
• On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$
• Rationality of vertex operator superalgebras with rational conformal weights
• Staggered modules of $N=2$ superconformal minimal models
• Bosonic Ghost Correlators: A Case Study