Open Orbits and Augmentations of Dynkin Diagrams

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dc.creatorFan, Sin Tsun Edward
dc.creatorLeung, Naichung Conan
dc.date2008-12-05
dc.date2009-03-08
dc.date.accessioned2026-07-07T12:49:33Z
dc.date.available2026-07-07T12:49:33Z
dc.descriptionGiven any representation V of a complex linear reductive Lie group G_0, we show that a larger semi-simple Lie group G with g=g_0 + V + V* + ..., exists precisely when V has a finite number of G_0-orbits. In particular, V admits an open G_0-orbit. Furthermore, this corresponds to an augmentation of the Dynkin diagram of g_0. The representation theory of g should be useful in describing the geometry of manifolds with stable forms as studied by Hitchin.
dc.descriptionAfter the first version was posted, we were informed that many of the results in it were obtained earlier by Kac, Rubenthaler and Vinberg. See Remark 1 for more details
dc.identifierhttps://arxiv.org/abs/0812.1078
dc.identifierhttp://arxiv.org/abs/0812.1078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222439
dc.subjectRepresentation Theory
dc.subjectDifferential Geometry
dc.subject22E46(Primary), 17B10 (Secondary)
dc.titleOpen Orbits and Augmentations of Dynkin Diagrams
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