Expanding the quasisymmetric Macdonald polynomials in the fundamental basis

Abstract

The quasisymmetric Macdonald polynomials G γ (X;q,t) were recently introduced by the first and second authors with Haglund, Mason, and Williams in [3] to refine the symmetric Macdonald polynomials P λ (X;q,t) with the property that G γ (X;0,0) equals QS γ (X), the quasisymmetric Schur polynomial of [9]. We derive an expansion for G γ (X;q,t) in the fundamental basis of quasisymmetric functions.