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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Crystal structures arising from representations of $GL(m|n)$
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by Jonathan Kujawa PDF
Represent. Theory 10 (2006), 49-85 Request permission


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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Additional 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