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

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We 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.
22 Pages, 1 Figure

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Representation Theory, Differential Geometry, 53D17, 17B10, 14J17

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http://salesiana.dossiersoluciones.com/handle/123456789/112906

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605660
 http://arxiv.org/abs/math/0605660

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arXiv