  We establish a direct connection between the representation theories of Lie
algebras and Lie superalgebras (of type A) via Fock space reformulations of
their Kazhdan-Lusztig theories. As a consequence, the characters of
finite-dimensional irreducible modules of the general linear Lie superalgebra
are computed by the usual parabolic Kazhdan-Lusztig polynomials of type A. In
addition, we establish closed formulas for canonical and dual canonical bases
for the tensor product of any two fundamental representations of type A.
