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A combinatorial formula for non-symmetric Macdonald polynomials

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arxiv math/0601693 v3 pith:UUVZZWMY submitted 2006-01-28 math.CO math.QA

J. Haglund , M. Haiman , N. Loehr This is my paper · ORCID
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We give a combinatorial formula for the non-symmetric Macdonald polynomials E_{\mu}(x;q,t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J_{\mu}(x;q,t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop, that characterizes the non-symmetric Macdonald polynomials.

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Cited by 5 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. Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems

    hep-th 2026-01 unverdicted novelty 7.0 of 10

    For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.

  3. 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.

  4. Twisted Cherednik spectrum as a $q,t$-deformation

    hep-th 2026-01 unverdicted novelty 6.0 of 10

    The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.

  5. 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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