Leclerc's irreducible-factor conjecture for Richardson varieties

Let $G$ be a semisimple algebraic group, let $N$ be its maximal unipotent subgroup, and let $\Rich_v^w$ be the open Richardson variety associated to $v\leq w$ in the Weyl group. For each $r\in[m]$, let $\vec f_r\in\mathbb{C}[N]$ be the regular function introduced in the construction, and let $J_{\mathbf{v}}^\circ$ be the associated index set. Leclerc's irreducible-factor conjecture. There exists a unique family $(F_r)_{r\in J_{\mathbf{v}}^\circ}$ of irreducible elements of $\mathbb{C}[N]$ such that, for each $r\in[m]$,

$$\vec f_r=\prod_{j\in J_{\mathbf{v}}^\circ:\,j\geq r}F_j^{p_{r,j}}$$

for some nonnegative integers $p_{r,j}\geq0$ satisfying $p_{r,r}=1$ for all $r\in J_{\mathbf{v}}^\circ$. The conjecture extends Leclerc's simply laced construction to arbitrary types and is open even when $G$ is simply laced.