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A diagrammatic approach to Ocneanu cells

Presented by: 
Stephen Bigelow University of California, Santa Barbara
Date: 
Monday 23rd January 2017 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons