Yan's conjecture on isotropy groups of simple derivations

Let $k$ be a field and let $R_n=k[x_1,\ldots,x_n]$. A $k$-derivation $d$ of $R_n$ is simple if $R_n$ has no proper nonzero ideal $I$ such that $d(I)\subseteq I$. The isotropy group of $d$ is

$$\operatorname{Aut}(R_n)_d=\{\varphi\in\operatorname{Aut}(R_n):\varphi\circ d=d\circ\varphi\}.$$

A translation is an automorphism of $R_n$ induced by $x_i\mapsto x_i+a_i$ for constants $a_i\in k$.

Yan's conjecture. If $d$ is a simple derivation of $R_n$, then $\operatorname{Aut}(R_n)_d$ is conjugate in $\operatorname{Aut}(R_n)$ to a subgroup of the group of translations.

This conjecture concerns the structure of isotropy groups for simple polynomial derivations. The source presents it as a conjecture proposed by D. Yan; the supplied material gives no resolution, so its status remains open.