The little desert? Some subfactors with index in the interval (5,3+\sqrt{5})
dc.contributor.author | Morrison, Scott | en_AU |
dc.contributor.author | Peters, Emily | en_AU |
dc.date.accessioned | 2012-10-09T02:14:05Z | |
dc.date.available | 2012-10-09T02:14:05Z | |
dc.date.created | 9/10/2012 | en_AU |
dc.description.abstract | 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}. 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.sponsorship | This research was funded through a grant. - ARC (DECRA award) and DARPA | en_AU |
dc.format.extent | 41 pages | en_AU |
dc.format.mimetype | application/pdf | en_AU |
dc.identifier.citation | Morrison, 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.uri | http://hdl.handle.net/1885/9433 | |
dc.language.iso | en_AU | en_AU |
dc.publisher | http://arxiv.org/ | en_AU |
dc.rights | Author holds copyright of the item (from submission email 6/09/2012) | en_AU |
dc.source.uri | http://arxiv.org/abs/1205.2742 | en_AU |
dc.subject | subfactors | en_AU |
dc.subject | planar algebras | en_AU |
dc.subject | fusion categories | en_AU |
dc.title | The little desert? Some subfactors with index in the interval (5,3+\sqrt{5}) | en_AU |
dc.type | Working/Technical Paper | en_AU |
dcterms.accessRights | Open Access | en_AU |
dcterms.dateAccepted | 2012-05-12 | |
local.contributor.authoremail | scott.morrison@anu.edu.au | en_AU |
local.contributor.authoruid | u5228111 | en_AU |
local.identifier.uidSubmittedBy | u5259801 | en_AU |
local.publisher.url | http://arxiv.org | en_AU |
local.type.status | Submitted Version | en_AU |