One-W-type modules for rational Cherednik algebra and cuspidal two-sided
cells

We classify the simple modules for the rational Cherednik algebra that are
irreducible when restricted to W, in the case when W is a finite Weyl group.
The classification turns out to be closely related to the cuspidal two-sided
cells in the sense of Lusztig. We compute the Dirac cohomology of these modules
and use the tools of Dirac theory to find nontrivial relations between the
cuspidal Calogero-Moser cells and the cuspidal two-sided cells.