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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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Quotients of representation rings
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by Hans Wenzl PDF
Represent. Theory 15 (2011), 385-406 Request permission

Abstract:

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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Additional Information
  • Hans Wenzl
  • Affiliation: Department of Mathematics, University of California San Diego, La Jolla California 92093-0112
  • MR Author ID: 239252
  • Email: hwenzl@ucsd.edu
  • 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: https://doi.org/10.1090/S1088-4165-2011-00401-5
  • MathSciNet review: 2801174