1-supertransitive subfactors with index at most 6.2

Abstract:

We classify subfactors by three invariants of increasing complexity: the index, the principal graph, and the standard invariant. The standard invariant is a unitary 2-category which generalizes the representation category of a (quantum) group, and thus we think of subfactors as objects which encode quantum symmetries.  In one sense, subfactors of small index are the simplest examples of subfactors, and we have a complete classification of their standard invariants to index 5.

I will discuss recent joint work with Liu and Morrison which classifies standard invariants of 1-supertransitive subfactors without intermediates with index in $(3+\sqrt{5},6.2)$. We show there are exactly 3 examples corresponding to $SO(3)_q$ at a root of unity and two "twisted" variations.