The super Artin basis conjecture for complex reflection groups

Let $G=G(m,1,n)$ act diagonally on the superalgebra ${\mathbb C}[{\bf x},\theta_1,\ldots,\theta_n]$, where the $x_i$ commute and the $\theta_i$ anticommute. Define the super coinvariant algebra

$$\operatorname{SRG}_{m,n}=\frac{{\mathbb C}[{\bf x},\theta_1,\ldots,\theta_n]}{\langle {\mathbb C}[{\bf x},\theta_1,\ldots,\theta_n]^G_+\rangle}.$$

For $T\subseteq[n]$, let $\beta(T)$ be the weak composition constructed from the $(m,|[n]\setminus T|)$-staircase as in the source, and define the super Artin set

$${\mathcal S}{\mathcal A}_{m,n}=\{ {\bf x}^\alpha\theta_T\mid T\subseteq[n]\text{ and }\alpha\leq\beta(T)\}.$$

Super Artin basis conjecture. The set ${\mathcal S}{\mathcal A}_{m,n}$ is a basis for $\operatorname{SRG}_{m,n}$.

This is a conjectural super analogue of the Artin basis for the ordinary coinvariant algebra. The paper presents Hilbert-series calculations in the extreme theta degrees as evidence, but the asserted basis result remains unproved in the supplied text.