Nakamura's G-Hilbert space conjecture in dimension three

Let $G$ be any finite subgroup of $\operatorname{SL}(3,\mathbb{C})$, and let $\mathcal{H}^G(\mathbb{C}^3)$ denote the $G$-Hilbert scheme. Nakamura's conjecture. The space $\mathcal{H}^G(\mathbb{C}^3)$ is a crepant resolution of $\mathbb{C}^3/G$. The conjecture is a three-dimensional form of the expectation that the Hilbert scheme of $G$-clusters provides a canonical crepant resolution of a quotient singularity; it was proved for abelian $G$ by Nakamura, while the non-abelian case was still described as in progress in the source.