Annihilator-generator conjecture for powers of central arrangement polynomials

Let $Q$ be a central arrangement polynomial, let $D_n$ be the ring of differential operators, let $I(Q)$ and $I_s(Q)$ be the recursively defined ideals generated by the operators $P_{i,j}(Q')$ in the source, and let $\mathcal E$ denote the Euler vector field.

Annihilator-generator conjecture. For any central arrangement $Q$,

$$\operatorname{ann}_{D_n}(Q^{-1})=I(Q)+\langle \mathcal E+k\rangle,$$

and

$$\operatorname{ann}_{D_n[s]}(Q^s)=I_s(Q)+\langle \mathcal E-ks\rangle.$$

The assertion gives explicit generators for the annihilators of $Q^{-1}$ and $Q^s$; the source provides no resolution in the supplied material.