An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models

TL;DR

This paper presents an explicit series representation for symmetric polynomials that serve as eigenfunctions of Calogero-Sutherland models and extends this to deformed models, enhancing analytical understanding.

Contribution

It introduces a new explicit analytic series for symmetric polynomials related to Calogero-Sutherland eigenfunctions and generalizes it to deformed models.

Findings

Explicit series representation for symmetric polynomials

Extension to eigenfunctions of deformed Calogero-Sutherland models

Improved analytical tools for Calogero-Sutherland type models

Abstract

We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero-Sutherland type models. We also indicate a generalisation of this result to polynomials which give the eigenfunctions of so-called 'deformed' Calogero-Sutherland type models.