Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials

TL;DR

This paper introduces a supersymmetric extension of Jack polynomials with fermionic variables, providing new mathematical tools and explicit models for supersymmetric Calogero-Moser-Sutherland systems.

Contribution

It constructs Jack superpolynomials as eigenfunctions of the supersymmetric CMS model and develops the Lax formulation, Dunkl operators, and conserved charges for these models.

Findings

Explicit examples of Jack superpolynomials are provided.

New Lax formulation and Dunkl operators for supersymmetric CMS models are derived.

Reformulation in exchange-operator formalism enhances analytical understanding.

Abstract

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version of the CMS models: the Lax formulation, the construction of the Dunkl operators and the explicit expressions for the conserved charges. The reformulation of the models in terms of the exchange-operator formalism is a crucial aspect of our analysis.