A recursion and a combinatorial formula for Jack polynomials

Details A recursion and a combinatorial formula for Jack polynomials A recursion and a combinatorial formula for Jack polynomials

1996-10-15

arxiv.org/abs/q-alg/9610016v1

Invent. Math. 128 (1997), 9-22

Mathematics

Quantum Algebra

Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX

Scientific paper

10.1007/s002220050134

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.

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