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 Representation Theory
Representation Theory
ISSN 1088-4165

     

Quotients of representation rings

Author(s): Hans Wenzl
Journal: Represent. Theory 15 (2011), 385-406.
MSC (2010): Primary 22E46
Posted: May 3, 2011
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Abstract | References | Similar articles | Additional information

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
Email: hwenzl@ucsd.edu

DOI: 10.1090/S1088-4165-2011-00401-5
PII: S 1088-4165(2011)00401-5
Received by editor(s): December 11, 2006
Received by editor(s) in revised form: January 11, 2011
Posted: May 3, 2011
Additional Notes: This work was partially supported by NSF grant DMS 0302437
Copyright of article: Copyright 2011, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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