Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients

TL;DR

This paper introduces new five-term identities for wreath Macdonald polynomials, enabling efficient tableau-based formulas for Pieri coefficients, significantly simplifying their computation.

Contribution

It provides novel five-term relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients, advancing computational methods in the field.

Findings

Derived new five-term identities for wreath Macdonald polynomials

Developed tableau formulas for Pieri coefficients

Enabled quick computation of monomial expansions

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.