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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.


BMW algebra, quantized coordinate algebra and type $C$ Schur–Weyl duality
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by Jun Hu
Represent. Theory 15 (2011), 1-62
Published electronically: January 10, 2011


We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra $\mathfrak {B}_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra $\mathfrak {sp}_{2m}$. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang in the symplectic case. As a byproduct, we show that, as a $\mathbb {Z}[q,q^{-1}]$-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by $A_q^{\mathbb {Z}}(g)$) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev–Reshetikhin–Takhtajan construction.
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Bibliographic Information
  • Jun Hu
  • Affiliation: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
  • Email:
  • Received by editor(s): March 8, 2009
  • Received by editor(s) in revised form: October 14, 2009
  • Published electronically: January 10, 2011
  • Additional Notes: This research was supported by National Natural Science Foundation of China (Project 10771014), the Program NCET and partly by an Australian Research Council discovery grant. The author also acknowledges the support of the Chern Institute of Mathematics during his visit in March of 2007.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 1-62
  • MSC (2000): Primary 17B37, 20C20; Secondary 20C08
  • DOI:
  • MathSciNet review: 2754334