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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Crystal structures arising from representations of $GL(m|n)$
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by Jonathan Kujawa
Represent. Theory 10 (2006), 49-85
Published electronically: February 16, 2006


This paper provides results on the modular representation theory of the supergroup $GL(m|n).$ Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation theory of a modular analogue of the Bernstein-Gelfand-Gelfand category $\mathcal {O}$. In particular, we obtain a linkage principle and describe the effect of certain translation functors on irreducible supermodules. Furthermore, our approach accounts for the fact that $GL(m|n)$ has non-conjugate Borel subgroups and we show how Serganova’s odd reflections give rise to canonical crystal isomorphisms.
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Bibliographic Information
  • Jonathan Kujawa
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 720815
  • Email:
  • Received by editor(s): November 17, 2003
  • Received by editor(s) in revised form: January 3, 2006
  • Published electronically: February 16, 2006
  • Additional Notes: Research was supported in part by NSF grant DMS-0402916
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 10 (2006), 49-85
  • MSC (2000): Primary 20C20, 05E99; Secondary 17B10
  • DOI:
  • MathSciNet review: 2209849