Bonnafé's conjecture on symplectic-leaf closures of fixed-point Calogero–Moser spaces

Let $W$ be a complex reflection group, let $\tau$ be a finite-order element of the normalizer of $W$ in ${\mathrm{GL}}_{\mathbb{C}}(V)$, and let $c\in{\mathcal{C}}$ satisfy $\tau(c)=c$. Let ${\mathcal{Z}}_c$ be the Calogero–Moser space, let ${\mathcal{Z}}_c^\tau$ be its reduced fixed-point subvariety, and let ${\mathcal{L}}$ be a symplectic leaf of ${\mathcal{Z}}_c^\tau$ with closure $\overline{{\mathcal{L}}}$. Bonnafé's conjecture. The normalization $\overline{{\mathcal{L}}}^{\mathrm{nor}}$ is isomorphic, as a Poisson variety endowed with a ${\mathbb{C}}^\times$-action, to a Calogero–Moser space associated with another pair $(V_{\mathcal{L}},W_{\mathcal{L}})$ and a parameter $k_{\mathcal{L}}\in\aleph(W_{\mathcal{L}})$. This conjecture concerns the structure of symplectic leaves in fixed-point subvarieties and is cited from earlier work; the supplied text does not state a general resolution.