Cuspidal Calogero-Moser and Lusztig families for Coxeter groups
Representation Theory
2016-06-20 v3 Algebraic Geometry
Group Theory
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1505.00486,
title = {Cuspidal Calogero-Moser and Lusztig families for Coxeter groups},
author = {Gwyn Bellamy and Ulrich Thiel},
journal= {arXiv preprint arXiv:1505.00486},
year = {2016}
}
Comments
Final version to appear in J. Algebra. In V3: minor additions and corrections