Kleinian singularity classification conjecture for full-support Harish-Chandra bimodules

Let $Y=\mathbb{C}^2/\Gamma$, where $\Gamma$ is a finite subgroup of $\operatorname{SL}_2(\mathbb{C})$, and let $\mathfrak{h}_\Gamma^*$ be the Cartan space associated with the ADE type of $\Gamma$. For $c\in (\mathbb{C}\Gamma)_1^\Gamma$, let $\lambda_c\in\mathfrak{h}_\Gamma^*$ be the corresponding quantization parameter, and write $W^a_\Gamma=W_\Gamma\ltimes\Lambda_r$ for the affine Weyl group, where $\Lambda_r$ is the root lattice. A full-support Harish-Chandra bimodule means an irreducible Harish-Chandra bimodule whose associated variety is all of $Y$. Kleinian full-support classification conjecture. For each $c\in(\mathbb{C}\Gamma)_1^\Gamma$, there is a minimal normal subgroup $\Gamma_c\subset\Gamma$ such that $W^a_\Gamma\lambda_c$ contains $\lambda_{c'}$ with $c'\in\mathbb{C}\Gamma_c\subset\mathbb{C}\Gamma$. The irreducible Harish-Chandra $\mathcal{A}_{\lambda_c}$-bimodules with full support are in bijection with the irreducible representations of $\Gamma/\Gamma_c$. This conjectural classification would determine the full-support Harish-Chandra bimodules for quantizations of Kleinian singularities; the source gives no resolution status for the claims.