# Some remarks on non-symmetric interpolation Macdonald polynomials

## TL;DR

This paper establishes elementary identities and duality relations for non-symmetric interpolation Macdonald polynomials, enhancing understanding and providing new tools for their application in binomial formulas.

## Contribution

It introduces new elementary identities and a duality for non-symmetric interpolation Macdonald polynomials, expanding theoretical understanding and potential applications.

## Key findings

- Derived elementary identities relating different types of non-symmetric interpolation Macdonald polynomials
- Established a duality property for these polynomials
- Applied results to binomial formulas involving the polynomials

## Abstract

We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of these results, in particular for binomial formulas involving non-symmetric interpolation Macdonald polynomials.