The fundamental-group conjecture for open Richardson varieties

Let $G$ be a semisimple algebraic group with Weyl group $W$, simple roots $\Delta$, and flag variety $G/B$. For $v\in W$, let $\mathring X_{\operatorname{{\rm id}}}^v$ denote the open Richardson variety, and define

$$\Gamma(v)=\\{\alpha\in\Delta\mid s_\alpha\leq v\\}.$$

Fundamental-group conjecture. For every $v\in W$,

$$\pi_1(\mathring X_{\operatorname{{\rm id}}}^v)=\mathbb{Z}^{|\Gamma(v)|}.$$

This expectation arises by viewing $\mathring X_{\operatorname{{\rm id}}}^v$ as the complement in the affine space $\mathbb{C}^{\ell(v)}$ of the Richardson divisors $X_{s_\alpha}^v$ for $\alpha\in\Gamma(v)$. The proposed description of the fundamental group depends on the corresponding general affine-plane sections satisfying the stated smoothness and transversality hypotheses; the source provides no resolution of the expectation.