Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients
Combinatorics
2025-07-11 v3 Quantum Algebra
Representation Theory
Abstract
We present a variety of new identities involving operators in the theory of wreath Macdonald polynomials. One such family of identities gives five-term relations, analogous to the one given by Garsia and Mellit for the modified Macdonald polynomials. As a consequence, we generate tableau formulas for wreath Macdonald Pieri coefficients, which give an incredibly quick way of computing their monomial expansions.
Keywords
Cite
@article{arxiv.2505.15606,
title = {Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients},
author = {Marino Romero and Joshua Jeishing Wen},
journal= {arXiv preprint arXiv:2505.15606},
year = {2025}
}
Comments
v3 28 pp. Fixed typos and expanded introduction. Comments welcome!