Cuspidal Calogero-Moser and Lusztig families for Coxeter groups

JOURNAL OF ALGEBRA

卷:462

Article

Bellamy, Gwyn¹  Thiel, Ulrich² 

[1] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QW, Lanark, Scotland

[2] Univ Stuttgart, Fachbereich Math, Inst Algebra & Zahlentheorie, Lehrstuhl Algebra, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Complex reflection groups;    Hecke algebras;    Cherednik algebras;    Calogero-Moser spaces;    Symplectic leaves;   

DOI  :  10.1016/j.jalgebra.2016.06.003

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free