Shuffle approach to wreath Pieri operators

Joshua Jeishing Wen

Shuffle approach to wreath Pieri operators

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arxiv 2402.06007 v1 pith:TBBGEMLN submitted 2024-02-08 math.QA math.COmath.RT

Joshua Jeishing Wen This is my paper · ORCID

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keywords wreathmacdonaldpolynomialsalgebracomputeformulaspieriquantum

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We describe a way to study and compute Pieri rules for wreath Macdonald polynomials using the quantum toroidal algebra. The Macdonald pairing can be naturally generalized to the wreath setting, but the wreath Macdonald polynomials are no longer collinear with their duals. We establish the relationship between these dual polynomials and the quantum toroidal algebra, and we outline a way to compute norm formulas. None of the aforementioned formulas are successfully computed in this paper.

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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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