On the Calogero-Moser space associated with dihedral groups II. The equal parameter case

TL;DR

This paper advances the understanding of Calogero-Moser spaces linked to dihedral groups by providing explicit equations, analyzing the Poisson structure, and exploring the Lie algebra and group actions in the equal parameter case.

Contribution

It offers detailed explicit equations and structural insights into Calogero-Moser spaces for dihedral groups with equal parameters, extending prior theoretical work.

Findings

Explicit equations for the space are derived.

Information about the Poisson bracket structure is provided.

The Lie algebra and SL_2(C) action are characterized.

Abstract

We continue the study of Calogero-Moser spaces associated with dihedral groups by investigating in more details the equal parameter case: we obtain explicit equations, some informations about the Poisson bracket, the structure of the Lie algebra associated with the cuspidal point and the action of $SL_2(\mathbb{C})$.