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Quotients of representation rings. (English) Zbl 1246.22016

Author’s 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.

MSC:

22E46 Semisimple Lie groups and their representations
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