  The aim of this paper is to generalize several aspects of the recent work of
Leclerc-Thibon and Varagnolo-Vasserot on the canonical bases of the level 1
q-deformed Fock spaces due to Hayashi. Namely, we define canonical bases for
the higher-level q-deformed Fock spaces of Jimbo-Misra-Miwa-Okado and establish
a relation between these bases and (parabolic) Kazhdan-Lusztig polynomials for
the affine Weyl group of type $A^{(1)}_{r-1}.$ As an application we derive an
inversion formula for a sub-family of these polynomials. This article is an
extended version of math.QA/9901032
