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Congruence subgroups and generalized Frobenius-Schur Indicators

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2010

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Ng, Siu-Hung

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http://nbn-resolving.de/urn:nbn:de:bsz:352-127603
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https://doi.org/10.1007/s00220-010-1096-6
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Communications in Mathematical Physics. 2010, 300(1), pp. 1-46. ISSN 0010-3616. Available under: doi: 10.1007/s00220-010-1096-6

Zusammenfassung

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.

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510 Mathematik

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ISO 690NG, Siu-Hung, Peter SCHAUENBURG, 2010. Congruence subgroups and generalized Frobenius-Schur Indicators. In: Communications in Mathematical Physics. 2010, 300(1), pp. 1-46. ISSN 0010-3616. Available under: doi: 10.1007/s00220-010-1096-6
BibTex
@article{Ng2010Congr-12760,
  year={2010},
  doi={10.1007/s00220-010-1096-6},
  title={Congruence subgroups and generalized Frobenius-Schur Indicators},
  number={1},
  volume={300},
  issn={0010-3616},
  journal={Communications in Mathematical Physics},
  pages={1--46},
  author={Ng, Siu-Hung and Schauenburg, Peter}
}
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