  We have two constructions of the level-$(0,1)$ irreducible representation of
the quantum toroidal algebra of type $A$. One is due to Nakajima and
Varagnolo-Vasserot. They constructed the representation on the direct sum of
the equivariant K-groups of the quiver varieties of type $\hat{A}$. The other
is due to Saito-Takemura-Uglov and Varagnolo-Vasserot. They constructed the
representation on the q-deformed Fock space introduced by Kashiwara-Miwa-Stern.
  In this paper we give an explicit isomorphism between these two
constructions. For this purpose we construct simultaneous eigenvectors on the
q-Fock space using nonsymmetric Macdonald polynomials. Then the isomorphism is
given by corresponding these vectors to the torus fixed points on the quiver
varieties.
