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On centralizer algebras for spin representations. (English) Zbl 1295.17014

The author gives a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups. This is expounded in terms of non-standard \(q\)-deformations of orthogonal Lie algebras in the case of even-dimensional algebras. However, for odd-dimensional case, the situation becomes somewhat complicated and hence only a certain subalgebras are considered. In the classical case, for which \(q=1\), the respective relations reduce to those of Lie algebra, as one would expect.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
22E46 Semisimple Lie groups and their representations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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