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A geometric construction for permutation equivariant categories from modular functors

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Abstract

Let G be a finite group. Given a finite G-set \(\cal{X}\) and a modular tensor category \(\cal{C}\), we construct a weak G-equivariant fusion category \(\cal{C}^{\cal{X}}\), called the permutation equivariant tensor category. The construction is geometric and uses the formalism of modular functors. As an application, we concretely work out a complete set of structure morphisms for \(\mathbb{Z}/2\)-permutation equivariant categories, finishing thereby a program we initiated in an earlier paper.

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  1. Organisationseinheit Mathematik, Universität Hamburg Bereich Algebra und Zahlentheorie, Bundesstraβe 55, D-20 146, Hamburg, Germany

    T. Barmeier & C. Schweigert

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  1. T. Barmeier
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  2. C. Schweigert
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Correspondence to T. Barmeier.

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Barmeier, T., Schweigert, C. A geometric construction for permutation equivariant categories from modular functors. Transformation Groups 16, 287–337 (2011). https://doi.org/10.1007/s00031-011-9132-y

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  • DOI: https://doi.org/10.1007/s00031-011-9132-y

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