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- W2111608844 abstract "We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via generalized Frobenius-Schur indicators. The set of all equivariant indicators admits a natural action of the modular group. Using the properties of equivariant indicators, we prove a congruence subgroup theorem for modular categories. As a consequence, all modular representations of a modular category have finite images, and they satisfy a conjecture of Eholzer. In addition, we obtain two formulae for the generalized indicators, one of them a generalization of Bantay's second indicator formula for a rational conformal field theory. This formula implies a conjecture of Pradisi-Sagnotti-Stanev, as well as a conjecture of Borisov-Halpern-Schweigert." @default.
- W2111608844 created "2016-06-24" @default.
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- W2111608844 date "2010-08-26" @default.
- W2111608844 modified "2023-10-12" @default.
- W2111608844 title "Congruence Subgroups and Generalized Frobenius-Schur Indicators" @default.
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- W2111608844 doi "https://doi.org/10.1007/s00220-010-1096-6" @default.
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