## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F.R. Jones’ 60th Birthday. Scott Morrison and David Pennys, eds. Proceedings of the Centre for Mathematics and its Applications, v. 46. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2017), 143 - 168

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1487646026

**Mathematical Reviews number (MathSciNet)**

MR3635670

**Zentralblatt MATH identifier**

06990153

#### Citation

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