The generalized image conjecture for orthogonal-polynomial differential operators

Let $B\subset\mathbb R^n$, let $w(z)$ and $\{u_\alpha\mid\alpha\in\mathbb N^n\}$ be the data of an orthogonal-polynomial system, with the variables written as $z$. Assume that the orthogonal polynomials are obtained through the stated Rodrigues-type equation for commuting differential operators $\Lambda=(\Lambda_1,\ldots,\Lambda_n)$ in a localization of $\mathbb C[z]$. Define

$$\operatorname{Im}'\Lambda=\mathbb C[z]\cap\sum_{i=1}^n\Lambda_i\mathbb C[z].$$

The generalized image conjecture. The subspace $\operatorname{Im}'\Lambda$ is a Mathieu subspace of $\mathbb C[z]$. The paper notes that this generalizes the image conjecture and proves some cases, but the general claim is not resolved in the supplied text.