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

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

2002-03-07

arxiv.org/abs/math/0203069v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

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.

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