Lifting shadings on symmetrically self-dual subfactor planar algebras
Lifting shadings on symmetrically self-dual subfactor planar algebras
In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary fusion categories.This nishes the proof that there are unitary fusion categories with fusion graphs 4442 and 3333.Planar algebras have proven to be …