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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra $\mathfrak{gl}(m\vert n)$


Author: Jonathan Brundan
Journal: J. Amer. Math. Soc. 16 (2003), 185-231
MSC (2000): Primary 17B10
DOI: https://doi.org/10.1090/S0894-0347-02-00408-3
Published electronically: October 16, 2002
MathSciNet review: 1937204
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Abstract: We compute the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak{gl}(m\vert n)$, and determine ${\operatorname{Ext}}$'s between simple modules in the category of finite dimensional representations. We formulate conjectures for the analogous results in category $\mathcal O$. The combinatorics parallels the combinatorics of certain canonical bases over the Lie algebra $\mathfrak{gl}(\infty)$.


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Additional Information

Jonathan Brundan
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: brundan@darkwing.uoregon.edu

DOI: https://doi.org/10.1090/S0894-0347-02-00408-3
Received by editor(s): March 12, 2002
Received by editor(s) in revised form: September 25, 2002
Published electronically: October 16, 2002
Additional Notes: Research partially supported by the NSF (grant no. DMS-0139019)
Article copyright: © Copyright 2002 American Mathematical Society