A recursion and a combinatorial formula for Jack polynomials
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Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating the symmetric Jack polynomials with the non-symmetric ones. These formulas are then implemented by a closed expression of symmetric and non-symmetric Jack polynomials in terms of certain tableaux. The main application is a proof of a conjecture of Macdonald stating certain integrality and positivity properties of Jack polynomials.
Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX
Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX