Abstract
We give a proof using so-called fusion rings andqq-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ringGr(O(∞))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 ofGl(N)Gl(N)toO(N)O(N)andSp(N)Sp(N)as well as detailed information about the structure of theqq-Brauer algebras in the nonsemisimple case for certain specializations.
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