Cuspidal Calogero–Moser and Lusztig families for Coxeter groups

Abstract

The goal of this paper is to compute the cuspidal Calogero–Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the symplectic leaves of the associated Calogero–Moser space and then by classifying certain “rigid” modules. Numerical evidence suggests that there is a very close relationship between Calogero–Moser families and Lusztig families. Our classification shows that, additionally, the cuspidal Calogero–Moser families equal cuspidal Lusztig families for the infinite families of Coxeter groups.