The q-harmonic coincidence conjecture for G(m,p,n)

Let $m,n\in\mathbb{N}$, let $p$ divide $m$, and let $G(m,p,n)$ be the complex reflection group contained in $G(m,n)$. Its $q$-harmonic space is defined using the $q$-deformed operators for $G(m,n)$ together with the undeformed operator $e_n(\partial_X)^{m/p}$, where $e_n(\mathbf{x})=x_1\cdots x_n$. The q-harmonic coincidence conjecture. The $q$-harmonic polynomials for $G(m,1,n)$, as defined above, coincide with those for $G(m,n)$. This conjecture would support the choice not to deform the generator $e_n^{m/p}$; the source notes that it is proved for $n=2$ and $\ell=1$ in the discussed setting.