The full exceptional collection conjecture for odd symplectic flag varieties

Let $V$ be a vector space of dimension $2n+1$ equipped with a skew-symmetric form of maximal rank $2n$, and let odd symplectic flag varieties be defined analogously to the odd isotropic Grassmannians. The odd symplectic flag variety conjecture. Derived categories of odd symplectic flag varieties admit full exceptional collections. These varieties are close to homogeneous varieties and provide a natural extension of the exceptional-collection problem; the source describes the assertion as very plausible, but does not give a general construction or resolution.