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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra $\mathfrak {gl}(m|n)$
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by Jonathan Brundan PDF
J. Amer. Math. Soc. 16 (2003), 185-231 Request permission

Abstract:

We compute the characters of the finite dimensional irreducible representations of the Lie superalgebra $\mathfrak {gl}(m|n)$, 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
  • 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)
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 185-231
  • MSC (2000): Primary 17B10
  • DOI: https://doi.org/10.1090/S0894-0347-02-00408-3
  • MathSciNet review: 1937204