Affine Hecke Algebras and Macdonald Polynomials

Abstract

This article is intended to be a survey on recent developments in symmetric and nonsymmetric Macdonald polynomials from the viewpoint of affine and double affine Hecke algebras. We also include an application of (double) affine Hecke algebras to the description of symmetries in Macdonald polynomials. In this article, we consider the Macdonald polynomials of type A n-1 exclusively to simplify the presentation, while a considerable part of the statements below has been extended to arbitrary root systems.