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A diagrammatic approach to Ocneanu cells

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OASW01 - Structure of operator algebras: subfactors and fusion categories

Kuperberg's SU(3) spider has “web” diagrams with oriented strands and trivalent vertices. A closed web evaluates to a real number, which can be thought of as a weighted sum of certain ways to “colour” the faces of the web. The weighting here is defined using Ocneanu cells, which were explicitly calculated in a 2009 paper by Evans and Pugh. I will describe a diagrammatic way to recover their calculation in the simplest case of the A series. Each strand of a web becomes a parallel pair of coloured strands, and each vertex becomes three coloured strands that connect up the three incoming pairs of coloured strands.

This talk is part of the Isaac Newton Institute Seminar Series series.

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