A planar algebra construction of the Haagerup subfactor

Understand

Most known examples of subfactors occur in families, coming from algebraic objects such as groups, quantum groups and rational conformal field theories.

• The Haagerup subfactor is the smallest index finite-depth subfactor which does not occur in one of these families.
• In this paper we construct the planar algebra associated to the Haagerup subfactor, which provides a new proof of the existence of the Haagerup subfactor.
• Our technique is to find the Haagerup planar algebra as a singly generated subfactor planar algebra, contained inside of a graph planar algebra.