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A recursion and a combinatorial formula for Jack polynomials

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arxiv q-alg/9610016 v1 pith:ZF5NJVG2 submitted 1996-10-15 q-alg math.QA

Friedrich Knop , Siddhartha Sahi This is my paper · ORCID
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keywords polynomialsjacknon-symmetriccertainformulaformulasrecursionsymmetric
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cherednik integrable system: eigenfunctions at generic eigenvalues

    hep-th 2026-07 conditional novelty 7.0 of 10

    Generic Cherednik eigenfunctions are N!-branched power series obtained by analytic continuation of factorized skew non-symmetric Macdonald coefficients.

  2. Generating twisted Cherednik eigenfunctions

    hep-th 2026-02 conditional novelty 6.0 of 10

    Twisted Macdonald polynomials are generated recursively from a ground state by creation and permutation moves, proving three conjectures about their coefficients.

  3. Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$

    hep-th 2026-07 accept novelty 4.5 of 10

    Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting auto...

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