Conjecture on Borel subalgebra conjugacy classes in the Jacobson–Witt algebra

Let $\mathfrak{g}=W_n$ be the Jacobson–Witt algebra of rank $n$ over the field $\mathbb{F}$, where $W_n$ is the derivation algebra of $\mathbb{F}[x_1,\ldots,x_n]/(x_1^p,\ldots,x_n^p)$. Borel subalgebra conjugacy conjecture. There are $n+1$ conjugacy classes of Borel subalgebras in $\mathfrak{g}$ under the action of the automorphism group of $\mathfrak{g}$. This is motivated by the classification of Cartan subalgebras of $W_n$ into $n+1$ conjugacy classes. The conjecture proposes an analogous classification for Borel subalgebras; its resolution is not established in the supplied text.