A rigidity result for extensions of braided tensor C*-categories derived from compact matrix quantum groups

Abstract

Let G be a classical compact Lie group and G_μthe associated compact matrix quantum group deformed by a positive parameter μ(or a nonzero and real μin the type A case). It is well known that the category Rep(G_μ) of unitary f.d. representations of G_μis a braided tensor C*-category. We show that any braided tensor *-functor from Rep(G_μ) to another braided tensor C*-category with irreducible tensor unit is full if |μ|\neq 1. In particular, the functor of restriction to the representation category of a proper compact quantum subgroup, cannot be made into a braided functor. Our result also shows that the Temperley--Lieb category generated by an object of dimension >2 can not be embedded properly into a larger category with the same objects as a braided tensor C*-subcategory.

19 pages; published version, to appear in CMP; for a more detailed exposition see v2

References in corpus (3)

• Tensor categories: A selective guided tour
• On Superselection Theory of Quantum Fields in Low Dimensions
• On the Jones index values for conformal subnets

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