Quadratic Algebra associated with Rational Calogero-Moser Models

TL;DR

This paper demonstrates the universal quadratic algebra structure underlying quantum rational Calogero-Moser models for all root systems, extending previous results known for A type systems.

Contribution

It establishes a universal quadratic algebra framework for quantum rational Calogero-Moser models across all root systems, generalizing prior A type specific findings.

Findings

Quadratic algebra structure confirmed for all root systems.

Universal algebraic framework for superintegrability.

Extension of known results from A type to all root systems.

Abstract

Classical Calogero-Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r-1 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebra structure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebra structure for quantum rational Calogero-Moser models based on any root systems.