Character and dimension formulae for general linear superalgebra

The generalized Kazhdan–Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is then 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.