Skip to Main Content

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.

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 $GL(m|n)$
HTML articles powered by AMS MathViewer

by Jonathan Kujawa PDF
Represent. Theory 10 (2006), 49-85 Request permission

Abstract:

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.
References
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20C20, 05E99, 17B10
  • Retrieve articles in all journals with MSC (2000): 20C20, 05E99, 17B10
Additional Information
  • Jonathan Kujawa
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 720815
  • Email: kujawa@math.uga.edu
  • 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: https://doi.org/10.1090/S1088-4165-06-00219-6
  • MathSciNet review: 2209849