Revista de la
Unión Matemática Argentina
Regular automorphisms and Calogero–Moser families
Cédric Bonnafé

Volume 68, no. 2 (2025), pp. 519–533    

Published online (final version): October 8, 2025

https://doi.org/10.33044/revuma.3143

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Abstract

We study the subvariety of fixed points of an automorphism of a Calogero–Moser space induced by a regular element of finite order of the normalizer of the associated complex reflection group $W$. We determine some of (and conjecturally all) the ${\mathbb{C}}^\times$-fixed points of its unique irreducible component of maximal dimension in terms of the character table of $W$. This 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 [Pure Appl. Math. Q. 21 no. 1 (2025), 131–200].

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