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

J. Fuchs·A. Ch. Ganchev·K. Szlachanyi·P. Vecsernyes
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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.

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J. Fuchs, A. Ch. Ganchev, K. Szlachanyi, P. Vecsernyes. 1998-03-26. S_4-symmetry of 6j-symbols and Frobenius-Schur indicators in rigid monoidal C^*-categories. https://doi.org/10.1063/1.532778

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