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Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition

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arxiv 1012.4199 v3 pith:F4RV6I5B submitted 2010-12-19 math.QA hep-thmath.RT

Yi-Zhi Huang , James Lepowsky , Lin Zhang This is my paper · ORCID
classification math.QAhep-thmath.RT
keywords intertwiningcategoryconditionlogarithmicmapsparttensortheory
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This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part V), we study products and iterates of intertwining maps and of logarithmic intertwining operators and we begin the development of our analytic approach.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ribbon categories of weight modules for affine $\mathfrak{sl}_2$ at admissible levels

    math.QA 2024-11 accept novelty 8.0 of 10

    Rigidity is proven for the braided tensor category of finitely-generated weight modules of affine sl2 at all admissible levels, upgrading it to a ribbon category.

  2. Tensor structure on the module category of the triplet superalgebra $\mathcal{{SW}}(m)$

    math.QA 2024-12 conditional novelty 7.0 of 10

    For each m, the tensor supercategory on SW(m)-mod is rigid, all simple and projective modules are self-dual, and the fusion ring is generated by one simple module X2.

  3. How are pseudo-$q$-traces related to (co)ends?

    math.QA 2025-08 conditional novelty 6.0 of 10

    The pseudo-q-trace construction is shown to be the same, through the sewing-factorization theorem, as the categorical end over the module category, proving conjectures of Gainutdinov-Runkel and Arike-Nagatomo.

  4. A basis theorem for Genus-One Conformal Blocks and modular invariance of intertwining operators

    math.QA 2025-08 unverdicted novelty 6.0 of 10

    Trace functions of intertwining operators form a global frame of genus-one conformal blocks, yielding a uniform proof of modular invariance for rational vertex operator algebras.

  5. Twisted intertwining operators and tensor products of (generalized) twisted modules

    math.QA 2025-01 conditional novelty 6.0 of 10

    New constructions and an analytic characterization of P(z)-tensor products and G-crossed braiding isomorphisms for twisted modules of a vertex operator algebra.

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