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AUTOMORPHISMS AND SYMPLECTIC LEAVES OF CALOGERO–MOSER SPACES

Part of: Rings and algebras arising under various constructions Local theory

Published online by Cambridge University Press:  17 October 2022

CÉDRIC BONNAFÉ
CÉDRIC BONNAFÉ*
Affiliation:
IMAG, Université de Montpellier, CNRS, Montpellier, France
*
e-mail: cedric.bonnafe@umontpellier.fr
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Abstract

We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero–Moser space induced by an element of finite order of the normalizer of the associated complex reflection group. We give a parametrization à la Harish-Chandra of its symplectic leaves (generalizing earlier works of Bellamy and Losev). This result is inspired by the mysterious relations between the geometry of Calogero–Moser spaces and unipotent representations of finite reductive groups, which is the theme of another paper, C. Bonnafé [‘Calogero–Moser spaces vs unipotent representations’, Pure Appl. Math. Q., to appear, Preprint, 2021, arXiv:2112.13684].

Keywords

reflection groupsCalogero–Moser spacessymplectic leaves

MSC classification

Primary: 14B05: Singularities 16S80: Deformations of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 115 , Issue 1 , August 2023 , pp. 26 - 57
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author is partly supported by the ANR: Projects Nos. ANR-16-CE40-0010-01 (GeRepMod) and ANR-18-CE40-0024-02 (CATORE).

Communicated by Benjamin Martin

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