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

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

2009-06-23

arxiv.org/abs/0906.4307v2

Munster J. Math. 2 (2009), 95-142

Mathematics

Operator Algebras

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

Scientific paper

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.

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