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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Super duality and Kazhdan-Lusztig polynomials

Authors: Shun-Jen Cheng, Weiqiang Wang and R. B. Zhang
Journal: Trans. Amer. Math. Soc. 360 (2008), 5883-5924
MSC (2000): Primary 17B10; Secondary 17B37, 20C08
Published electronically: June 26, 2008
MathSciNet review: 2425696
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Abstract: 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$.

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Additional Information

Shun-Jen Cheng
Affiliation: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529

Weiqiang Wang
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904

R. B. Zhang
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia

PII: S 0002-9947(08)04447-4
Received by editor(s): October 17, 2006
Published electronically: June 26, 2008
Article copyright: © Copyright 2008 American Mathematical Society