Rank-three semiorthogonal decomposition conjecture for moduli spaces of vector bundles

Let $C$ be a smooth projective curve of genus $g\geq 2$, let $L$ be a line bundle of degree $1$ on $C$, and let $M(3,L)$ be the moduli space of rank-three stable vector bundles on $C$ with determinant $L$. Write $C_k$ for the $k$-th symmetric power of $C$, and let $D(X)$ denote the bounded derived category of coherent sheaves on $X$. Rank-three semiorthogonal decomposition conjecture. The derived category of $M(3,L)$ should have a semiorthogonal decomposition

$$D(M(3,L))=\langle \cdots,D(C_{k_1}\times C_{k_2}),D(C_{k_1}\times C_{k_2}),\cdots,D(C_{g-1}\times C_{g-1})\rangle,$$

where $(k_1,k_2)$ is a pair of nonnegative integers satisfying $k_1+k_2<2(g-1)$ or $k_1+k_2=2(g-1)$ and $k_1<g-1$. The same source conjectures analogous decompositions for the corresponding Chow and Voevodsky motives and for the Karoubian-completed Fukaya category. These proposed decompositions are intended to make derived, motivic, and Fukaya-category structures reflect one another; the source gives no evidence of resolution.