Constructing the extended Haagerup planar algebra
Author(s)Bigelow, Stephen; Peters, Emily; Morrison, Scott; Snyder, Noah
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We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range (4,3+√3), which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein-theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein-theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram. This is the published version of arXiv:0909.4099 [math.OA].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Bigelow, Stephen et al. “Constructing the Extended Haagerup Planar Algebra.” Acta Mathematica 209.1 (2012): 29–82.
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