Walton's conjecture on simple representations of 3-dimensional Sklyanin algebras

Let $A$ be a 3-dimensional Sklyanin algebra, and let $\tau$ be a torsion point of order $n$ on its associated elliptic curve, with $(n,3)=3$. Consider the simple finite-dimensional representations of $A$. Walton's conjecture. The simple representations of $A$ have dimensions $n$, $\frac{n}{3}$, or $1$, and the simple representations of dimension $\frac{n}{3}$ form a $3:1$-cover over three lines intersecting in a unique point. The paper states that this conjecture is verified using the connection between fat point modules, stabilizers of simple representations, and $\mathbb{C}^*$-families of non-trivial simple representations; the cited source is the original formulation of the claim.