On symplectic leaves and integrable systems in standard complex semisimple Poisson-Lie groups

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We provide an explicit description of symplectic leaves of a simply connected connected semisimple complex Lie group equipped with the standard Poisson-Lie structure. This sharpens previously known descriptions of the symplectic leaves as connected components of certain varieties. Our main tool is the machinery of twisted generalized minors. They also allow us to present several quasi-commuting coordinate systems on every symplectic leaf. As a consequence, we construct new completely integrable systems on some special symplectic leaves.
13 pages

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Quantum Algebra, Symplectic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/63514

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0203069
 http://arxiv.org/abs/math/0203069

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arXiv