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We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A 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 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 A .
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Cheng et al. (2008) studied this question.
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