Expanding the quasisymmetric Macdonald polynomials in the fundamental basis

Abstract

The quasisymmetic Macdonald polynomials $G_{\gamma }(X;q,t)$ were recently introduced by the first and second authors with Haglund, Mason, and Williams in [3] to refine the symmetric Macdonald polynomials $P_{\lambda }(X;q,t)$ with the property that $G_{\gamma }(X;0,0)$ equals $Q{S}_{\gamma }(X)$, the quasisymmetric Schur polynomial of [9]. We derive an expansion for $G_{\gamma }(X;q,t)$ in the fundamental basis of quasisymmetric functions.

15 pages, 1 figure