A recursion and a combinatorial formula for Jack polynomials
(joint work with Siddhartha Sahi)
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.
Appeared in: Inventiones Mathematicae
128 (1997) 9-22
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Last updated: October 26, 2000