# 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…

## 46 Citations

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