 
Summary: arXiv:0909.4099v2[math.OA]23Feb2011
Constructing the extended Haagerup planar algebra
STEPHEN BIGELOW
SCOTT MORRISON
EMILY PETERS
NOAH SNYDER
URLs: http://www.math.ucsb.edu/~bigelow/ http://tqft.net/
http://euclid.unh.edu/~eep and http://math.berkeley.edu/~nsnyder
Email: bigelow@math.ucsb.edu, scott@tqft.net,
eep@euclid.unh.edu and nsnyder@math.columbia.edu
Abstract We construct a new subfactor planar algebra, and as a corollary a
new subfactor, with the `extended Haagerup' principal graph pair. This com
pletes 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
