Constructing the extended Haagerup planar algebra
Stephen Bigelow, Scott Morrison, Emily Peters, Noah Snyder

TL;DR
This paper constructs a new subfactor planar algebra with the extended Haagerup principal graph, completing the classification of certain subfactors, and provides explicit descriptions and evaluation algorithms for it.
Contribution
It introduces a new subfactor planar algebra with the extended Haagerup graph, proving its uniqueness and providing explicit skein theoretic and algebraic descriptions.
Findings
Constructed a new subfactor planar algebra with extended Haagerup graph
Proved the uniqueness of this subfactor planar algebra
Developed an explicit evaluation algorithm for diagrams
Abstract
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 , 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra
