Graphical characterization of modular invariance
Leonard Hardiman
TL;DR
This paper explores the graphical representation of modular invariance in tensor categories, providing a new characterization of modular invariant matrices through annular graphical calculus.
Contribution
It introduces a novel graphical characterization of modular invariant matrices in the context of modular tensor categories using annular calculus.
Findings
Characterization of modular invariant matrices via graphical calculus
Representation theory of tube categories related to modular invariance
New insights into the structure of modular tensor categories
Abstract
For a given modular tensor category we study representations of the corresponding tube category whose isomorphism classes are modular invariant matrices. In particular, we provide a characterization of these representations in terms of the annular graphical calculus of the tube category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology