I am looking for a proof or counterexample for following assertion 



> 
> Each [coadjoint orbit](http://ncatlab.org/nlab/show/coadjoint+orbit) of a compact connected Lie group $G$ admits
>  a [$G$-invariant generalized complex structure](http://arxiv.org/pdf/0712.2627.pdf) (In sense of Nigel
>  Hitchin)
> 
> 
> 



Each coadjoint orbit of a compact connected Lie group $G$ admits a $G$-invariant generalized complex structure
In 1950s A. Borel, R. Bott, J. L. Koszul, F. Hirzebruch et al. investigated the coadjoint orbits as complex
homogeneous manifolds. It was proven that each coadjoint orbit of a compact
connected Lie group $G$ admits a canonical G-invariant complex structure and the
only (within homotopies) $G$-invariant Kählerian metrics.


Reference: Bott R. The Geometry and Representation Theory of Compact Lie Groups, In: Representation
Theory of Lie Groups, London Mathematical Society Lecture Note Series,
Cambridge Univ. Press, 34 (1979) 65–90.


