Dimension conjecture for non-Kähler families of (1,2)-symplectic metrics on full flag manifolds

Let $F(n)$ be a full flag manifold, and consider families of (1,2)-symplectic metrics on $F(n)$ that are different from the family of Kähler metrics. Dimension conjecture. All such families of (1,2)-symplectic metrics on $F(n)$ are $n$-dimensional. This conjecture concerns the parameter-space dimension of the non-Kähler families of (1,2)-symplectic metrics; no resolution or further qualification is supplied in the text.