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arXiv · q-alg/9610016

A recursion and a combinatorial formula for Jack polynomials

Friedrich Knop·Siddhartha Sahi
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Abstract

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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Friedrich Knop, Siddhartha Sahi. 1996-10-15. A recursion and a combinatorial formula for Jack polynomials. https://doi.org/10.1007/s002220050134

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