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.

Final version to appear in J. Algebra. In V3: minor additions and corrections

References in corpus (5)

• Finite dimensional representations of rational Cherednik algebras
• Cellules de Calogero-Moser
• Restricted rational Cherednik algebras
• One-W-type modules for rational Cherednik algebra and cuspidal two-sided cells
• Cuspidal representations of rational Cherednik algebras at t=0

Cited by in corpus (5)

• Highest weight theory for finite-dimensional graded algebras with triangular decomposition
• Restricted rational Cherednik algebras
• Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
• Dirac induction for rational Cherednik algebras
• On Calogero-Moser cellular characters for imprimitive complex reflection groups