Transactions of the American Mathematical Society

Author(s): Shun-Jen Cheng; Weiqiang Wang; R. B. Zhang
Journal: Trans. Amer. Math. Soc. 360 (2008), 5883-5924.
MSC (2000): Primary 17B10; Secondary 17B37, 20C08
Posted: June 26, 2008
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Abstract: We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type

) 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

. In addition, we establish closed formulas for canonical and dual canonical bases for the tensor product of any two fundamental representations of type

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 17B10, 17B37, 20C08

Shun-Jen Cheng
Affiliation: Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529
Email: chengsj@math.sinica.edu.tw

Weiqiang Wang
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email: ww9c@virginia.edu

R. B. Zhang
Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
Email: rzhang@maths.usyd.edu.au

DOI: 10.1090/S0002-9947-08-04447-4
PII: S 0002-9947(08)04447-4
Received by editor(s): October 17, 2006
Posted: June 26, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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