In this [question](https://mathoverflow.net/questions/45004/kahler-structure-on-flag-manifolds) it is asked if every flag manifold can be given the structure of a Kähler manifold. In the first answer it is written 



> 
> Flag manifolds exhaust all compact homogeneous Kähler manifolds corresponding to a compact connected semi-simple Lie group
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> 
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What is the standard reference for this result?



Flag manifolds as homogeneous Kahler manifolds
Flag manifolds $G/C(S)$ even exhaust homogeneous *symplectic* manifolds of $G$: Borel-Weil ([1954](//zbmath.org/?q=an:0121.16203), Thm 1). Also restated with fewer details in ([1954](https://zbmath.org/?q=an:0058.16002), Thm 1).


