Finkelberg–Mirković reducedness conjecture for spherical Schubert varieties

Let $G$ be the group under consideration and let $\lambda$ be a dominant coweight. Let $\overline{\mathcal{Y}^\lambda}\subset\operatorname{Gr}_G$ be the moduli scheme of principal $G$-bundles on $\mathbb{P}^1$ with a trivialization on $\mathbb{A}^1$ satisfying the pole condition determined by $\lambda$, and let $\overline{\operatorname{Gr}^\lambda}$ be the corresponding spherical Schubert variety. Finkelberg–Mirković reducedness conjecture. The scheme $\overline{\mathcal{Y}^\lambda}$ is reduced. In particular,

$$\overline{\mathcal{Y}^\lambda}=\overline{\operatorname{Gr}^\lambda}.$$

The moduli description is set-theoretically correct, but reducedness is the issue needed to identify it scheme-theoretically with the spherical Schubert variety.