Transverse Poisson Structures to Adjoint orbits in semi-simple Lie algebras

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dc.creatorDamianou, Pantelis A.
dc.creatorSabourin, Herve
dc.creatorVanhaecke, Pol
dc.date2006-05-25
dc.date.accessioned2026-07-07T07:14:31Z
dc.date.available2026-07-07T07:14:31Z
dc.descriptionWe study the transverse Poisson structure to adjoint orbits in a complex semi-simple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen quasi-homogeneous coordinates the quasi-degree of the transverse Poisson structure is -2. In the particular case of {\emph subregular} nilpotent orbits we show that the structure may be computed by means of a simple determinantal formula, involving the restriction of the Chevalley invariants on the slice. In addition, using results of Brieskorn and Slodowy, the Poisson structure is reduced to a three dimensional Poisson bracket, intimately related to the simple rational singularity that corresponds to the subregular orbit.
dc.description22 Pages, 1 Figure
dc.identifierhttps://arxiv.org/abs/math/0605660
dc.identifierhttp://arxiv.org/abs/math/0605660
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112906
dc.subjectRepresentation Theory
dc.subjectDifferential Geometry
dc.subject53D17, 17B10, 14J17
dc.titleTransverse Poisson Structures to Adjoint orbits in semi-simple Lie algebras
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