Develops a generic algorithm for decomposing transfer-matrix spaces into Temperley-Lieb modules for fusion-category lattice models and computes modular transformations of irreducible TL characters at primitive roots of unity.
A field guide to categories with $A_n$ fusion rules
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abstract
We collate information about the fusion categories with $A_n$ fusion rules. This note includes the classification of these categories, a realisation via the Temperley-Lieb categories, the auto-equivalence groups (both braided and tensor), identifications of the subcategories of invertible objects, and explicit descriptions of the Drinfeld centres. The first section describes the classification of these categories (as monoidal, dagger, pivotal, and braided categories). The second section describes the properties of these categories.
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math-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Non-invertible symmetries and modular invariance in lattice models
Develops a generic algorithm for decomposing transfer-matrix spaces into Temperley-Lieb modules for fusion-category lattice models and computes modular transformations of irreducible TL characters at primitive roots of unity.