PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Hyperplane arrangements associated to symplectic quotient singularities

Volume 116 / 2018

Gwyn Bellamy, Travis Schedler, Ulrich Thiel Banach Center Publications 116 (2018), 25-45 MSC: Primary: 14E15; Secondary: 14E30, 16S80, 17B63. DOI: 10.4064/bc116-2

Abstract

We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory of restricted rational Cherednik algebras. We explain some of the interesting consequences of this identification for the representation theory of restricted rational Cherednik algebras. We also show that the Calogero–Moser space is smooth if and only if the Calogero–Moser families are trivial. We describe the arrangements of CM-hyperplanes associated to several exceptional complex reflection groups, some of which are free.

Authors

  • Gwyn BellamySchool of Mathematics and Statistics
    University of Glasgow
    University Place
    Glasgow G12 8QQ, Scotland
    e-mail
  • Travis SchedlerDepartment of Mathematics
    Imperial College London
    South Kensington Campus
    London SW7 2AZ, United Kingdom
    e-mail
  • Ulrich ThielSchool of Mathematics and Statistics
    University of Sydney
    Sydney, NSW 2006, Australia
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image