  Let Q be an affine quiver of type A. Let C be the associated generalized
Cartan matrix. Let U^- be the negative part of the quantized enveloping algebra
attached to C. In terms of perverse sheaves on the moduli space of
representations of a quiver, Lusztig constructed U geometrically and gave a
canonical basis B of U^- at the same time. The simple perverse sheaves which
enter B are defined abstractly in general. In Lusztig's paper [L2], by using
McKay's correspondence, he gave a description of these canonical basis elements
in affine cases, i.e. specifying the corresponding supports and local systems.
But the chosen orientations and the number of vertices of the quiver are not
arbitrary. In this paper we generalized the description in [L2] for arbitrary
orientations and vertices in the case of type A by using the theory of
representations of quivers.
