On Haagerup's list of potential principal graphs of subfactors

TL;DR

This paper proves that only the smallest two graphs in Haagerup's list of potential principal graphs of subfactors are realizable, resolving the last open case in a prior classification effort.

Contribution

It conclusively shows that all but the two smallest graphs in Haagerup's list cannot be realized as principal graphs of subfactors.

Findings

Only the smallest two graphs are realizable.

All other graphs in Haagerup's list are not realized.

The remaining open case from previous work is settled.

Abstract

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.