The real loci of the Calogero-Moser spaces and the Shapiro-Shapiro conjecture

TL;DR

This paper discusses the real loci of Calogero-Moser spaces and their relation to the Shapiro-Shapiro conjecture, contributing to the understanding of algebraic structures and conjectures in mathematical physics.

Contribution

It introduces new insights into the structure of Calogero-Moser spaces and their connection to the Shapiro-Shapiro conjecture, advancing the mathematical theory in this area.

Findings

Clarified the structure of real loci in Calogero-Moser spaces

Linked Calogero-Moser spaces to the Shapiro-Shapiro conjecture

Provided new algebraic tools for analyzing rational Cherednik algebras

Abstract

This paper has been withdrawn by the authors; it is superceeded by the paper: The real loci of Calogero--Moser spaces, representations of rational Cherednik algebras and the Shapiro conjecture, by Iain Gordon, Emil Horozov, and Milen Yakimov, arXiv:0711.4336.