Infinite transitivity for Calogero-Moser spaces

TL;DR

This paper proves a conjecture that the automorphism group of certain Calogero-Moser spaces acts with high transitivity, revealing deep symmetry properties of these algebraic structures.

Contribution

It establishes that the automorphism group of a product of pairwise distinct Calogero-Moser spaces acts m-transitively for all m, confirming a conjecture by Berest-Eshmatov-Eshmatov.

Findings

Automorphism group acts m-transitively for all m on the product spaces.

Confirmed the conjecture of Berest-Eshmatov-Eshmatov.

Deepens understanding of symmetry in Calogero-Moser spaces.

Abstract

We prove the conjecture of Berest-Eshmatov-Eshmatov by showing that the group of automorphisms of a product of Calogero-Moser spaces $C_{n_i}$, where the $n_i$ are pairwise distinct, acts $m$-transitively for each $m$.