The binomial formula for nonsymmetric Macdonald polynomials

Abstract

Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beautiful expansion formula which can be viewed as a multivariable generalization of the q-binomial theorem. It is becoming clear that many interesting results in the symmetric setting can also be established in the nonsymmetric setting. In this paper, we prove the nonsymmetric analogue the binomial formula, and also discuss the limiting case of Jack polynomials.