The little desert? Some subfactors with index in the interval (5,3+\sqrt{5})

dc.contributor.authorMorrison, Scotten_AU
dc.contributor.authorPeters, Emilyen_AU
dc.date.accessioned2012-10-09T02:14:05Z
dc.date.available2012-10-09T02:14:05Z
dc.date.created9/10/2012en_AU
dc.description.abstractProgress 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.en_AU
dc.description.sponsorshipThis research was funded through a grant. - ARC (DECRA award) and DARPAen_AU
dc.format.extent41 pagesen_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.citationMorrison, S. & Peters, E. (2012) The little desert? Some subfactors with index in the interval (5,3+\sqrt{5}). arXiv:1205.2742 [math.OA]en_AU
dc.identifier.urihttp://hdl.handle.net/1885/9433
dc.language.isoen_AUen_AU
dc.publisherhttp://arxiv.org/en_AU
dc.rightsAuthor holds copyright of the item (from submission email 6/09/2012)en_AU
dc.source.urihttp://arxiv.org/abs/1205.2742en_AU
dc.subjectsubfactorsen_AU
dc.subjectplanar algebrasen_AU
dc.subjectfusion categoriesen_AU
dc.titleThe little desert? Some subfactors with index in the interval (5,3+\sqrt{5})en_AU
dc.typeWorking/Technical Paperen_AU
dcterms.accessRightsOpen Accessen_AU
dcterms.dateAccepted2012-05-12
local.contributor.authoremailscott.morrison@anu.edu.auen_AU
local.contributor.authoruidu5228111en_AU
local.identifier.uidSubmittedByu5259801en_AU
local.publisher.urlhttp://arxiv.orgen_AU
local.type.statusSubmitted Versionen_AU

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