Fields conjecture on the Frobenius characteristic of the superspace coinvariant ring

Let $SR_n$ be the bigraded superspace coinvariant ring with its natural $\mathfrak{S}_n$-action, and let $\operatorname{grFrob}(SR_n;q,z)$ denote its bigraded Frobenius characteristic. Let $C_{n,k}(\mathbf{x};q)$ be the symmetric function defined by

$$C_{n,k}(\mathbf{x};q)=\left.\Delta'_{e_{k-1}}e_n\right|_{t\to 0},$$

where $\Delta'_{e_{k-1}}$ is the primed Delta operator. Fields conjecture on the Frobenius characteristic. The bigraded Frobenius characteristic of $SR_n$ is

$$\operatorname{grFrob}(SR_n;q,z)=\sum_{k=1}^n z^{n-k}\cdot C_{n,k}(\mathbf{x};q).$$

This is the symmetric-function refinement of the predicted structure of $SR_n$, relating its graded representations to Delta-operator expressions; the supplied text gives no resolution status.