The Special Image Conjecture

Let $A={\mathbb C}[\xi,z]$, where $\xi=(\xi_1,\ldots,\xi_m)$ and $z=(z_1,\ldots,z_m)$ are two sets of commuting indeterminates. For each $i$, define ${\cal D}_i=\xi_i-\partial_{z_i}$, and set

$$\operatorname{Im}{\cal D}=\sum_{i=1}^m{\cal D}_iA.$$

A ${\mathbb C}$-linear subspace $M$ of $A$ is a Mathieu subspace if, for every $f\in A$, $f^k\in M$ for all $k\in\mathbb N_+$ implies that for every $g\in A$ there exists $K\in\mathbb N$ such that $gf^k\in M$ for all $k\ge K$. Special Image Conjecture. The image $\operatorname{Im}{\cal D}$ is a Mathieu subspace of $A$. The paper identifies this as the special image conjecture and relates it to the broader image-conjecture framework. No resolution is given in the supplied text.