Mikhail Kogan, Andrei Zelevinsky; On symplectic leaves and integrable systems in standard complex semisimple Poisson-Lie groups. Int Math Res Notices 2002; 2002 (32): 1685-1702. doi: 10.1155/S1073792802203050
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.