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arXiv · 1904.05015

Wreath Macdonald polynomials as eigenstates

Joshua Jeishing Wen
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Abstract

We show that the wreath Macdonald polynomials for $\mathbb{Z}/\ell\mathbb{Z}\wr\Sigma_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\mathfrak{q},\mathfrak{d}}(\ddot{\mathfrak{sl}}_\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials.

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BibTeXRIS

Joshua Jeishing Wen. 2019-04-10. Wreath Macdonald polynomials as eigenstates. https://doi.org/10.1007/s00029-025-01059-0

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