Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 037, 17 pages      math-ph/0703012      http://dx.doi.org/10.3842/SIGMA.2007.037
Contribution to the Proceedings of the Coimbra Workshop on Geometric Aspects of Integrable Systems

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

Martin Hallnäs
Department of Theoretical Physics, Albanova University Center, SE-106 91 Stockholm, Sweden

Received November 01, 2006, in final form February 05, 2007; Published online March 01, 2007

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.

Key words: quantum integrable systems; orthogonal polynomials; symmetric functions.

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