Orthogonal Symmetric Polynomials Associated with the Calogero Model
Hideaki Ujino
Abstract
The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a one-dimensional quantum integrable system with inverse-sine-square interactions. Inspired by the Rodrigues formula for the Jack polynomials, which form the orthogonal basis of the Sutherland model, recently found by Lapointe and Vinet, we construct the Rodrigues formula for the Hi-Jack (hidden-Jack) polynomials that form the orthogonal basis of the Calogero model.
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