Super duality and Kazhdan-Lusztig polynomials

@article{Cheng2004SuperDA,
  title={Super duality and Kazhdan-Lusztig polynomials},
  author={Shun-Jen Cheng and Weiqiang Wang and R. B. Zhang},
  journal={Transactions of the American Mathematical Society},
  year={2004},
  volume={360},
  pages={5883-5924}
}
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… 

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