Fixed points in smooth Calogero-Moser spaces

TL;DR

This paper proves that fixed point components under roots of unity actions in smooth Calogero-Moser spaces are isomorphic to other Calogero-Moser spaces linked to different reflection groups, revealing structural relationships.

Contribution

It establishes a new isomorphism between fixed point components and Calogero-Moser spaces for different reflection groups, deepening understanding of their geometric structure.

Findings

Fixed points under roots of unity form components isomorphic to other Calogero-Moser spaces.

The result links fixed point varieties to reflection groups beyond the original.

Provides a geometric framework for analyzing symmetries in Calogero-Moser spaces.

Abstract

We prove that every irreducible component of the fixed point variety under the action of $d$-th roots of unity in a smooth Caloger-Moser space is isomorphic to a Calogero-Moser space associated with another reflection group.