Differential equations and logarithmic intertwining operators for strongly graded vertex algebras. (English) Zbl 1414.17020
Summary: We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded vertex algebra under a certain finiteness condition and a condition related to the horizontal gradings. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory for such strongly graded generalized modules developed by Huang, Lepowsky and Zhang.
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
Keywords:
strongly graded vertex algebra; differential equations; \(C_1\)-cofiniteness condition; logarithmic intertwining operators; logarithmic tensor categoryReferences:
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