Super duality and Kazhdan-Lusztig polynomials
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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 $A$.References
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Additional Information
- 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
- MR Author ID: 339426
- 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
- Received by editor(s): October 17, 2006
- Published electronically: June 26, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 5883-5924
- MSC (2000): Primary 17B10; Secondary 17B37, 20C08
- DOI: https://doi.org/10.1090/S0002-9947-08-04447-4
- MathSciNet review: 2425696