A recursion and a combinatorial formula for Jack polynomials
q-alg
2008-02-03 v1 Quantum Algebra
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.
Cite
@article{arxiv.q-alg/9610016,
title = {A recursion and a combinatorial formula for Jack polynomials},
author = {Friedrich Knop and Siddhartha Sahi},
journal= {arXiv preprint arXiv:q-alg/9610016},
year = {2008}
}
Comments
Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX