Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs
David E. Evans, Mathew Pugh
TL;DR
This paper computes Ocneanu cells and Boltzmann weights for SU(3) ADE graphs, enabling the analysis of integrable models and subfactors related to SU(3) modular invariants, and proposing a new planar algebra framework.
Contribution
It determines the Ocneanu cells on all relevant SU(3) ADE graphs except one, facilitating the construction of integrable models and subfactor theories.
Findings
Computed Ocneanu cells for most SU(3) ADE graphs.
Enabled calculation of Boltzmann weights for integrable models.
Laid groundwork for SU(3) planar algebra development.
Abstract
We determine the cells, whose existence has been announced by Ocneanu, on all the candidate nimrep graphs except 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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology