A method to derive explicit formulas for an elliptic generalization of the Jack polynomials

Abstract

We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case.

14 pages, to appear in the proceedings of a workshop on "Jack, Hall-Littlewood and Macdonald polynomials", V.B. Kuznetsov and S. Sahi (eds.), Contemporary Mathematics, AMS

References in corpus (1)

• Algorithms to solve the Sutherland model

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