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Representation Theory

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Quotients of representation rings

Author: Hans Wenzl
Journal: Represent. Theory 15 (2011), 385-406
MSC (2010): Primary 22E46
Published electronically: May 3, 2011
MathSciNet review: 2801174
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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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Hans Wenzl
Affiliation: Department of Mathematics, University of California San Diego, La Jolla California 92093-0112
MR Author ID: 239252

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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.