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

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (8)

• The Calogero-Sutherland Model and Generalized Classical Polynomials
• A recursion and a combinatorial formula for Jack polynomials
• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Inversion of the Pieri formula for Macdonald polynomials
• Algorithms to solve the Sutherland model
• Explicit formulas for the generalized Hermite polynomials in superspace
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Cited by in corpus (2)

• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• A basis for the polynomial eigenfunctions of deformed Calogero-Moser-Sutherland operators