Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems

TL;DR

This paper introduces polynomials linked to the equilibrium positions of affine Toda-Sutherland systems, a class of integrable multi-particle models combining features of affine Toda and Sutherland systems.

Contribution

It determines the polynomials associated with equilibrium positions for all affine simple root systems, advancing understanding of these quasi-exactly solvable models.

Findings

Polynomials are explicitly derived for all affine simple root systems.

The work bridges affine Toda and Sutherland models.

Provides a comprehensive characterization of equilibrium configurations.

Abstract

An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a `cross' between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system. Polynomials describing the equilibrium positions of affine Toda-Sutherland systems are determined for all affine simple root systems.