Cuspidal Calogero-Moser and Lusztig families for Coxeter groups

Gwyn Bellamy; Ulrich Thiel

doi:10.1016/j.jalgebra.2016.06.003

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arXiv · 1505.00486

Cuspidal Calogero-Moser and Lusztig families for Coxeter groups

Gwyn Bellamy·Ulrich Thiel

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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.

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BibTeX RIS

Gwyn Bellamy, Ulrich Thiel. 2015-05-03. Cuspidal Calogero-Moser and Lusztig families for Coxeter groups. https://doi.org/10.1016/j.jalgebra.2016.06.003

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