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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.

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Quotients of representation rings
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by Hans Wenzl
Represent. Theory 15 (2011), 385-406
Published electronically: May 3, 2011


We give a proof using so-called fusion rings and $q$-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring $Gr(O(\infty ))$. This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to $\infty$. This in turn allows a detailed description of the quotient map in terms of a reflection group. As an application, one obtains a general description of the branching rules for the restriction of representations of $Gl(N)$ to $O(N)$ and $Sp(N)$ as well as detailed information about the structure of the $q$-Brauer algebras in the nonsemisimple case for certain specializations.
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Bibliographic Information
  • Hans Wenzl
  • Affiliation: Department of Mathematics, University of California San Diego, La Jolla California 92093-0112
  • MR Author ID: 239252
  • Email:
  • Received by editor(s): December 11, 2006
  • Received by editor(s) in revised form: January 11, 2011
  • Published electronically: May 3, 2011
  • Additional Notes: This work was partially supported by NSF grant DMS 0302437
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 385-406
  • MSC (2010): Primary 22E46
  • DOI:
  • MathSciNet review: 2801174