SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants

We complete the realization by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.

• Publication year

  2009

• Venue

  Reviews in Mathematical Physics

• Publication date

  2009-06-23

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1142/S0129055X09003761arXiv 0906.4252
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs

  2009influential reference
• A2-Planar Algebras I

  2009cited by this paper
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory

  2009cited by this paper
• A 2 -Planar Algebras II: Planar Modules

  2009influential reference
• Ising model and beyond

  2008cited by this paper
• Subfactor Realisation of Modular Invariants

  2003cited by this paper
• Fusion rules of modular invariants

  2002cited by this paper
• Critical Phenomena, Modular Invariants and Operator Algebras

  2002influential reference
• Modular invariants and subfactors

  2000influential reference
• The classification of subgroups of quantum SU(N)

  2000influential reference
• Modular Invariants from Subfactors:¶Type I Coupling Matrices and Intermediate Subfactors

  1999cited by this paper
• Chiral Structure of Modular Invariants for Subfactors

  1999cited by this paper
• On α-Induction, Chiral Generators and¶Modular Invariants for Subfactors

  1999cited by this paper
• Boundary conditions in rational conformal field theories

  1999influential reference
• Operator algebras and conformal field theory III. Fusion of positive energy representations of LSU(N) using bounded operators

  1998influential reference
• Quantum symmetries on operator algebras

  1998cited by this paper
• Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors I

  1998cited by this paper
• Modular Invariants, Graphs and α-Induction¶for Nets of Subfactors. III

  1998cited by this paper
• New Braided Endomorphisms from Conformal Inclusions

  1997cited by this paper
• Generalized Goodman–Harpe–Jones Construction of Subfactors, I

  1997cited by this paper
• Generalized Goodman–Harpe–Jones Construction of Subfactors, II

  1997cited by this paper
• Spiders for rank 2 Lie algebras

  1996cited by this paper
• Orbifold subfactors from Hecke algebras

  1994cited by this paper
• Nets of Subfactors

  1994cited by this paper
• DIMENSION GROUPS AND EMBEDDINGS OF GRAPH ALGEBRAS

  1994influential reference
• Operator Algebras and Conformal Field Theory

  1993cited by this paper
• The classification of affineSU(3) modular invariant partition functions

  1992cited by this paper
• SU($N$) Lattice Integrable Models Associated With Graphs

  1990cited by this paper
• Naturality in Conformal Field Theory

  1989cited by this paper
• Coxeter graphs and towers of algebras

  1989cited by this paper
• Hecke algebras of typeAn and subfactors

  1988cited by this paper
• Hecke algebras of type A n and subfactors

  1988cited by this paper
• State Models and the Jones Polynomial

  1987cited by this paper
• The A-D-E classification of minimal andA1(1) conformal invariant theories

  1987influential reference
• Dimensions and C*-algebras

  1981cited by this paper
• Dimensions and *-Algebras

  1981cited by this paper
• Critical phenomena.

  1971cited by this paper
• On induction

  1965cited by this paper

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  2023influential citation
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  2022influential citation
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  2016cites this paper
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• Alternative formulation for the operator algebra over the space of paths in a ADE $SU(3)$ graph

  2015cites this paper
• Spectral Measures for G2

  2015influential citation
• Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case

  2014cites this paper
• Essential paths space on ADE SU(3) graphs: A geometric approach

  2014influential citation
• Spectral measures for $Sp(2)$

  2014influential citation
• The Brauer-Picard group of the Asaeda-Haagerup fusion categories

  2012cites this paper
• Quantum Subgroups of the Haagerup Fusion Categories

  2012cites this paper
• SUBFACTOR REALIZATION OF MODULAR INVARIANTS: II

  2012cites this paper
• The twisted quantum double of modular data and subfactors

  2011cites this paper
• Quantum Subgroups of the Haagerup Fusion Categories

  2011cites this paper
• Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants

  2011influential citation
• The Nakayama Automorphism of the Almost Calabi-Yau Algebras Associated to SU(3) Modular Invariants

  2011cites this paper
• Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries

  2010cites this paper
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)

  2010influential citation
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  2010influential citation
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• The Nakayama permutation of the nimreps associated to SU(3) modular invariants

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  2009cites this paper
• A2-Planar Algebras I

  2009influential citation
• Spectral Measures for Sp (2)

  year unknowncites this paper