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 the nonsymmetric Macdonald polynomials.
Then the isomorphism is given by corresponding these vectors
to the torus fixed points on the quiver varieties.