  The generalized Kazhdan-Lusztig polynomials for the finite dimensional
irreducible representations of the general linear superalgebra are computed
explicitly. Using the result we establish a one to one correspondence between
the set of composition factors of an arbitrary $r$-fold atypical
$gl_{m|n}$-Kac-module and the set of composition factors of some $r$-fold
atypical $gl_{r|r}$-Kac-module. The result of Kazhdan-Lusztig polynomials is
also applied to prove a conjectural character formula put forward by van der
Jeugt et al in the late 80s. We simplify this character formula to cast it into
the Kac-Weyl form, and derive from it a closed formula for the dimension of any
finite dimensional irreducible representation of the general linear
superalgebra.
