Integrable Many-Body Systems of Calogero-Moser-Sutherland Type in High Dimension

TL;DR

This paper discovers new integrable many-body systems in high-dimensional spaces, expanding the class of known models and linking them to algebraic structures like Krichever-Novikov algebras.

Contribution

It introduces a new series of integrable many-body systems in high dimensions, connecting them to affine Krichever-Novikov algebras, and broadening the understanding of integrable models.

Findings

New integrable many-body systems in high dimensions identified

Connection established between these systems and Krichever-Novikov algebras

Part of a larger classification of integrable problems

Abstract

A new series of integrable cases of the many-body problem in many-dimensional spaces is found. That series appears as a part of the larger series of integrable problems, which are in 1-1 correspondence with Krichever-Novikov algebras of affine type (that is with pairs each one consisting of some finite root system and some Riemann surface of finite genus with two marked points).