## The little desert? Some subfactors with index in the interval (5,3 +v5)

### Description

Progress on classifying small index subfactors has revealed an almost empty landscape. In this paper we give some evidence that this desert continues up to index $3+\sqrt{5}$. There are two known quantum-group subfactors with index in this interval, and we show that these subfactors are the only way to realize the corresponding principal graphs. One of these subfactors is 1-supertransitive, and we demonstrate that it is the only 1-supertransitive subfactor with index between 5 and $3+\sqrt{5}$....[Show more]

Collections ANU Research Publications 2014 Journal article http://hdl.handle.net/1885/75184 International Journal of Mathematics 10.1142/S0129167X14500803