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

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

1998-03-26

arxiv.org/abs/physics/9803038v1

Physics

Mathematical Physics

21 pages + 16 pages with figures; LaTeX2e plus macro package XYpic; file with included pictures available as http://www.desy

Scientific paper

10.1063/1.532778

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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