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dc.contributor.authorKruglikov, Boris
dc.contributor.authorThe, Dennis
dc.date.accessioned2018-08-02T09:16:59Z
dc.date.available2018-08-02T09:16:59Z
dc.date.issued2014-09-14
dc.description.abstractThe infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when considering non-flat geometries, so a gap phenomenon arises. For general (regular, normal) parabolic geometries of type (G,P), we use Tanaka theory to derive a universal upper bound on the submaximal symmetry dimension. We use Kostant’s version of the Bott–Borel–Weil Theorem to show that this bound is in fact sharp in almost all complex and split-real cases by exhibiting (abstract) models. We explicitly compute all submaximal symmetry dimensions when G is any complex or split-real simple Lie group.en_US
dc.description.sponsorshipUiT The Arctic University of Norway Australian Research Councilen_US
dc.descriptionAccepted manuscript version. Published version available at <a href=https://doi.org/10.1515/crelle-2014-0072> https://doi.org/10.1515/crelle-2014-0072</a>.en_US
dc.identifier.citationKruglikov, B.S. & The, D. (2017). The gap phenomenon in parabolic geometries. Journal für die Reine und Angewandte Mathematik, 723, 153-215. https://doi.org/10.1515/crelle-2014-0072en_US
dc.identifier.cristinIDFRIDAID 1512412
dc.identifier.doi10.1515/crelle-2014-0072
dc.identifier.issn0075-4102
dc.identifier.issn1435-5345
dc.identifier.urihttps://hdl.handle.net/10037/13334
dc.language.isoengen_US
dc.publisherDe Gruyteren_US
dc.relation.journalJournal für die Reine und Angewandte Mathematik
dc.rights.accessRightsopenAccessen_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410en_US
dc.subjectSubmaximal symmetryen_US
dc.subjectparabolic geometryen_US
dc.subjectharmonic curvatureen_US
dc.subjectTanaka theoryen_US
dc.titleThe gap phenomenon in parabolic geometriesen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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