Skein Theory of Affine ADE Subfactor Planar Algebras

Abstract: The Kuperberg Program seeks to describe presentations of subfactor planar algebras in order to classify them and prove results about their corresponding categories purely diagrammatically. This program has been completed for index less than 4 and remains an area of ongoing research for index greater than 4. This talk will discuss the program at index 4. At this index, planar algebras other than Temperley-Lieb have an affine $A$, $D$, or $E$ principal graph. Categories corresponding to some of the affine A planar algebras are monoidally equivalent to cyclic pointed fusion categories. For affine $E_7$, to prove sufficiency of its presentation, we define a jellyfish algorithm. I will describe the jellyfish algorithm using a half braiding and discuss that it gives a well-defined surjective function onto $C$.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home