Difference operators for wreath Macdonald polynomials

TL;DR

This paper introduces explicit q-difference operators that act diagonally on wreath Macdonald P-polynomials, providing a new tool for their analysis in finitely many variables.

Contribution

It presents the first explicit construction of q-difference operators for wreath Macdonald polynomials, advancing understanding of their algebraic structure.

Findings

Operators act diagonally on wreath Macdonald P-polynomials

Explicit formulas for the q-difference operators

Enhances computational and theoretical analysis of these polynomials

Abstract

We give explicit $q$-difference operators acting diagonally on wreath Macdonald $P$-polynomials in finitely many variables.