A combinatorial formula for non-symmetric Macdonald polynomials

TL;DR

This paper presents a new combinatorial formula for non-symmetric Macdonald polynomials, extending previous work on symmetric polynomials and verified through a recurrence relation.

Contribution

It introduces a novel combinatorial formula for non-symmetric Macdonald polynomials, generalizing earlier interpretations for symmetric cases.

Findings

The formula accurately reproduces non-symmetric Macdonald polynomials.

Verification via Knop's recurrence confirms correctness.

Extends combinatorial understanding of Macdonald polynomials.

Abstract

We give a combinatorial formula for the non-symmetric Macdonald polynomials E_{\mu}(x;q,t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J_{\mu}(x;q,t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop, that characterizes the non-symmetric Macdonald polynomials.