Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
High Energy Physics - Theory
2009-11-07 v2 Condensed Matter
Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.hep-th/0103178,
title = {Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials},
author = {P. Desrosiers and L. Lapointe and P. Mathieu},
journal= {arXiv preprint arXiv:hep-th/0103178},
year = {2009}
}
Comments
Minor corrections in tables; 30 pages