Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

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

Retrieve articles in all journals with MSC (2000): 17B10, 17B37, 20C08


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
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: http://dx.doi.org/10.1090/S0002-9947-08-04447-4
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