A Combinatorial Formula for Nonsymmetric Macdonald Polynomials

Abstract

We give a combinatorial formula for the nonsymmetric Macdonald polynomials E μ ( x; q, t ). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J μ ( x; q, t ). We prove the new formula by verifying that it satisfies a recurrence, due to Knop and Sahi, that characterizes the nonsymmetric Macdonald polynomials.