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

Abstract

We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except ${\mathcal{E}}_4^{(12)}$ proposed by di Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This enables the Boltzmann weights to be computed for the corresponding integrable statistical mechanical models and provide the framework for studying corresponding braided subfactors to realise all the SU(3) modular invariants as well as a framework for a new SU(3) planar algebra theory.

46 pages, minor changes, to appear in Munster Journal of Mathematics

References in corpus (5)

• Condensate induced transitions between topologically ordered phases
• Random matrices, free probability, planar algebras and subfactors
• Subfactor realisation of modular invariants
• Spectral measures of small index principal graphs
• A2-Planar Algebras II: Planar Modules

Cited by in corpus (9)

• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
• A2-Planar Algebras II: Planar Modules
• 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
• Essential paths space on ADE SU(3) graphs: A geometric approach
• Classification of Module Categories for $SO(3{)}_{2m}$
• On the homology of almost Calabi-Yau algebras associated to SU(3) modular invariants
• Antisymmetric characters and Fourier duality