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On centralizer algebras for spin representations

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arxiv 1107.4183 v2 pith:RHAUHNCW submitted 2011-07-21 math.QA

Hans Wenzl This is my paper · ORCID
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keywords algebrascaserelationscentralizerrepresentationsalgebraappearboil
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We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations.

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  1. The quantum spin Brauer category

    math.QA 2025-04 accept novelty 7.0 of 10

    The quantum spin Brauer category is a braided diagrammatic category whose Karoubi completion covers all finite-dimensional U_q(so(N)) and U_q(o(N)) modules, including spin modules.

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