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Modular Data for the Extended Haagerup Subfactor

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Gannon, Terry; Morrison, Scott

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We compute the modular data (that is, the S and T matrices) for the centre of the extended Haagerup subfactor [BMPS12]. The full structure (i.e., the associativity data, also known as 6-j symbols or F matrices) still appears to be inaccessible. Nevertheless, starting with just the number of simple objects and their dimensions (obtained by a combinatorial argument in [MW14]) we find that it is surprisingly easy to leverage knowledge of the representation theory of SL(2,Z) into a complete...[Show more]

dc.contributor.authorGannon, Terry
dc.contributor.authorMorrison, Scott
dc.date.accessioned2020-12-20T20:57:20Z
dc.date.available2020-12-20T20:57:20Z
dc.identifier.issn0010-3616
dc.identifier.urihttp://hdl.handle.net/1885/218232
dc.description.abstractWe compute the modular data (that is, the S and T matrices) for the centre of the extended Haagerup subfactor [BMPS12]. The full structure (i.e., the associativity data, also known as 6-j symbols or F matrices) still appears to be inaccessible. Nevertheless, starting with just the number of simple objects and their dimensions (obtained by a combinatorial argument in [MW14]) we find that it is surprisingly easy to leverage knowledge of the representation theory of SL(2,Z) into a complete description of the modular data. We also investigate the possible character vectors associated with this modular data.
dc.description.sponsorshipScott Morrison was supported by a Discovery Early Career Research Award DE120100232, Discovery Projects ‘Subfactors and symmetries’ DP140100732 and ‘Low dimensional categories’ DP160103479 from the Australian Research Council, and DOD-DARPA grant HR0011-12-1-0009. Terry Gannon was supported by an NSERC Discovery grant; he thanks ANU for its generosity during two very pleasant visits.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherHarwood Academic Publishers
dc.rights© 2017 Springer-Verlag GmbH Germany
dc.sourceCommunications in Mathematical Physics
dc.titleModular Data for the Extended Haagerup Subfactor
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume356
dc.date.issued2017-09-30
local.identifier.absfor010599 - Mathematical Physics not elsewhere classified
local.identifier.ariespublicationu4351680xPUB200
local.type.statusPublished Version
local.contributor.affiliationGannon, Terry, University of Alberta
local.contributor.affiliationMorrison, Scott, College of Science, ANU
local.description.embargo2099-12-31
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage981
local.bibliographicCitation.lastpage1015
local.identifier.doi10.1007/s00220-017-3003-x
dc.date.updated2020-11-23T10:50:15Z
local.identifier.scopusID2-s2.0-85030151877
dc.relation.urihttp://purl.org/au-research/grants/arc/DE120100232
dc.relation.urihttp://purl.org/au-research/grants/arc/DP140100732
dc.relation.urihttp://purl.org/au-research/grants/arc/DP160103479
CollectionsANU Research Publications

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