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Wreath Macdonald operators

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arxiv 2211.03851 v3 pith:4TO7XSAD submitted 2022-11-07 math.QA math.COmath.RT

Daniel Orr , Mark Shimozono , Joshua Jeishing Wen This is my paper · ORCID
classification math.QAmath.COmath.RT
keywords operatorsmacdonaldpolynomialswreathactionalgebraarbitraryarise
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abstract

We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald $P$-polynomials; the eigenvalues are written in terms of elementary symmetric polynomials of arbitrary degree. Our operators arise from integral formulas for the action of the horizontal Heisenberg subalgebra in the vertex representation of the corresponding quantum toroidal algebra

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  1. Tesler identities for wreath Macdonald polynomials

    math.QA 2025-05 conditional novelty 7.0 of 10

    For r>2, an explicit operator identity (Tesler identity) relates each wreath Macdonald polynomial to a delta function and yields Macdonald-Koornwinder duality, evaluation, interpolation, Kostka, and bispectral results.

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