All factorizable Lie bialgebra structures on complex reductive Lie algebras were described by Belavin and Drinfeld. We classify the symplectic leaves of all related Poisson-Lie groups. A formula for their dimensions is also proved.
"Symplectic leaves of complex reductive Poisson-Lie groups." Duke Math. J. 112 (3) 453 - 509, 15 April 2002. https://doi.org/10.1215/S0012-9074-02-11233-2