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

We classify the simple modules for the rational Cherednik algebra H0,c 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, in the sense of Bellamy, and the cuspidal two-sided cells