Classification conjecture for invariant generalized complex structures on real flag manifolds

Let $\mathbb{F}_\Theta=K/K_\Theta$ be a real flag manifold, where $K$ is the acting compact group and $K_\Theta$ is the isotropy subgroup determined by $\Theta$. For a root system of type $C_l$, write $\Theta$ as a subset of the simple roots, with $\lambda_i$ denoting the standard root-coordinate notation.

Classification conjecture. A real flag manifold $\mathbb{F}_\Theta=K/K_\Theta$ admits a $K$-invariant generalized complex structure if and only if it is of type $C_l$ and

$$\Theta=lbrace \lambda_{d}-\lambda_{d+1},\cdots, \lambda_{l-1}-\lambda_{l}, 2\lambda_{l}rbrace$$

for $d>1$ odd.

This gives a proposed complete classification of real flag manifolds carrying invariant generalized complex structures. The supplied parser provides no resolution evidence, so the conjecture remains open.