The ideal conjecture for general affine-Grassmannian slices

Let $\Gr^{\overline{\lambda}}_\mu$ be the affine-Grassmannian slice in $\Gr_\mu$, and let $J^\lambda_\mu$ be the Poisson ideal of $\mathcal O(\Gr_\mu)$ generated by $\Delta_{\omega_i,\omega_i}^{(s)}$ for all $i\in I$ and $s>\langle\lambda-\mu,\omega_{i^*}\rangle$. The ideal conjecture. The ideal of $\Gr^{\overline{\lambda}}_\mu$ in $\mathcal O(\Gr_\mu)$ is $J^\lambda_\mu$. This extends the proposed ideal description from the base-point slice to arbitrary $\mu$ and is intended to make the slice accessible through its Poisson coordinate algebra; the source gives no proof or counterexample.