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I have often heard/read a statement (see, e.g., this MathOverflow question) equivalent to the following: Let $G$ be a connected Lie group and $(M,\omega)$ a connected and simply-connected symplectic ...

Let $M=G/H$ be a compact homogeneous space, $G$ a compact Lie Group and $H$ a closed subgroup. Is there some classification, akin to the Kaehler case, for which such manifolds admit a symplectic ...

In this question 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 ...

Let $H$ be a semisimple element of the Lie algebra $\mathfrak{g}$ of a semisimple Lie group $G$, and let $M:=\mathrm{Ad}_G(H)\subset\mathfrak{g}$ be the corresponding adjoint orbit. If we choose a ...

Let $G$ be a real semisimple Lie group (say $SL(2,\mathbb{R})$) and $H$ be its Cartan subgroup (say torus or diagonal subgroup of $SL(2,\mathbb{R})$). My questions is: it is always true that we have ...