Morrison, ScottPeters, Emily2012-10-092012-10-099/10/2012Morrison, S. & Peters, E. (2012) The little desert? Some subfactors with index in the interval (5,3+\sqrt{5}). arXiv:1205.2742 [math.OA]http://hdl.handle.net/1885/9433Progress 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}. Computer evidence shows that any other subfactor in this interval would need to have rank at least 38. We prove our uniqueness results by showing that there is a unique flat connection on each graph. The result on 1-supertransitive subfactors is proved by an argument using intermediate subfactors, running the `odometer' from the FusionAtlas` Mathematica package and paying careful attention to dimensions.This research was funded through a grant. - ARC (DECRA award) and DARPA41 pagesapplication/pdfen-AUAuthor holds copyright of the item (from submission email 6/09/2012)subfactorsplanar algebrasfusion categoriesThe little desert? Some subfactors with index in the interval (5,3+\sqrt{5})