Subfactor realisation of modular invariants

Abstract

We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D_5^(1). In particular for the double of S_3, 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors.

References in corpus (12)

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• Module categories over the Drinfeld double of a finite group
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• Module categories, weak Hopf algebras and modular invariants
• Critical Phenomena, modular invariants and operator algebras
• Modular invariants and subfactors
• (2+1)-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants
• Computations of Turaev-Viro-Ocneanu invariants of 3-manifolds from subfactors

Cited by in corpus (27)

• Correspondences of ribbon categories
• The exoticness and realisability of twisted Haagerup-Izumi modular data
• Module categories over the Drinfeld double of a finite group
• The fusion algebra of bimodule categories
• Twenty-five years of two-dimensional rational conformal field theory
• Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms
• On Frobenius algebras in rigid monoidal categories
• Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs
• Critical Phenomena, modular invariants and operator algebras
• Comments about quantum symmetries of SU(3) graphs
• SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants
• Phase boundaries in algebraic conformal QFT
• A remark on gapped domain walls between topological phases
• Higher Coxeter graphs associated to affine su(3) modular invariants
• Infinite index extensions of local nets and defects
• Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
• From modular invariants to graphs: the modular splitting method
• Constructing non-semisimple modular categories with local modules
• Modular Invariants and Twisted Equivariant K-theory
• Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants
• Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries
• Modular invariants for group-theoretical modular data. I
• A relative tensor product of subfactors over a modular tensor category
• Essential paths space on ADE SU(3) graphs: A geometric approach
• On a Connes Fusion Approach to Finite Index Extensions of Conformal Nets
• Alternative formulation for the operator algebra over the space of paths in a ADE $SU(3)$ graph
• Reducibility of quantum representations of mapping class groups