S_4-symmetry of 6j-symbols and Frobenius-Schur indicators in rigid monoidal C^*-categories

Abstract

We show that a left-rigid monoidal C^*-category with irreducible monoidal unit is also a sovereign and spherical category. Defining a Frobenius-Schur type indicator we obtain selection rules for the fusion coefficients of irreducible objects. As a main result we prove S_4-invariance of 6j-symbols in such a category.

21 pages + 16 pages with figures; LaTeX2e plus macro package XYpic; file with included pictures available as http://www.desy.de/~jfuchs/s4/s4.ps.gz

References in corpus (3)

• A Coassociative C*-Quantum Group with Non-Integral Dimensions
• The Frobenius-Schur indicator in Conformal Field Theory
• Mapping Class Group Representations and Generalized Verlinde Formula

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