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

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...

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Bibliographic Details
Published in:arXiv.org 1998-03
Main Authors: Fuchs, J, Ganchev, A Ch, Szlachanyi, K, Vecsernyes, P
Format: Article
Language:English
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.9803038