A generalization of Newton's identity and Macdonald functions

TL;DR

This paper generalizes Newton's identity for symmetric functions, providing a unified approach to establish the existence of key polynomial families like Hall-Littlewood, Jack, and Macdonald polynomials, and offers a simple proof for a specific Macdonald function formula.

Contribution

It introduces a generalized Newton identity that unifies the existence proofs of several important symmetric function families and simplifies the proof of a Macdonald function formula.

Findings

Unified method for existence of Hall-Littlewood, Jack, and Macdonald polynomials

Simplified proof of Jing-J"ozefiak formula for two-row Macdonald functions

Generalization of Newton's identity for symmetric functions

Abstract

A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Hall-Littlewood, Jack and Macdonald polynomials. We also give a simple proof of the Jing-J\"ozefiak formula for two-row Macdonald functions.