The ungraded Orlik–Terao representation conjecture

Let $M_n$ and $D_n$ be the graded $S_n$-representations in the main conjecture, and let $\overline{M}_n$ and $\overline{D}_n$ denote the corresponding ungraded representations. Let $Z_n$ be the cyclic subgroup of $S_n$ acting on $S_n$ by right multiplication.

Ungraded Orlik–Terao representation conjecture. There exists an isomorphism of $S_n$-representations

$$\overline{M}_n\cong\overline{D}_n\cong\operatorname{Ind}_{Z_n}^{S_n}(\operatorname{triv})\cong\mathbb{C}[S_n/Z_n],$$

where $Z_n$ acts on $S_n$ via right multiplication.

This conjecture gives an explicit description of the common ungraded representation and was verified computationally through $n=10$ in the source. No general proof or disproof is stated.