## Proceedings of the Centre for Mathematics and its Applications

### Existence of the $AH + 2$ subfactor

Pinhas Grossman

#### Abstract

We give two different proofs of the existence of the $AH + 2$ subfactor, which is a 3-supertransitive self-dual subfactor with index $\frac{9+\sqrt{17}}{2}$. The first proof is a direct construction using connections on graphs and intertwiner calculus for bimodule categories. The second proof is indirect, and deduces the existence of $AH + 2$ from a recent alternative construction of the Asaeda-Haagerup subfactor and fusion combinatorics of the Brauer-Picard groupoid.

#### Article information

Dates
First available in Project Euclid: 21 February 2017

Grossman, Pinhas. Existence of the $AH + 2$ subfactor. Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F.R. Jones’ 60th Birthday, 143--168, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2017. https://projecteuclid.org/euclid.pcma/1487646026