Congruence subgroups and generalized Frobenius-Schur Indicators


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NG, Siu-Hung, Peter SCHAUENBURG, 2010. Congruence subgroups and generalized Frobenius-Schur Indicators. In: Communications in Mathematical Physics. 300(1), pp. 1-46. ISSN 0010-3616

@article{Ng2010Congr-12760, title={Congruence subgroups and generalized Frobenius-Schur Indicators}, year={2010}, doi={10.1007/s00220-010-1096-6}, number={1}, volume={300}, issn={0010-3616}, journal={Communications in Mathematical Physics}, pages={1--46}, author={Ng, Siu-Hung and Schauenburg, Peter} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:available rdf:datatype="">2011-07-20T09:19:57Z</dcterms:available> <bibo:uri rdf:resource=""/> <dc:rights>deposit-license</dc:rights> <dc:contributor>Schauenburg, Peter</dc:contributor> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <dc:language>eng</dc:language> <dc:contributor>Ng, Siu-Hung</dc:contributor> <dcterms:rights rdf:resource=""/> <dcterms:bibliographicCitation>First publ. in: Communications in Mathematical Physics 300 (2010), 1, pp. 1-46</dcterms:bibliographicCitation> <dcterms:title>Congruence subgroups and generalized Frobenius-Schur Indicators</dcterms:title> <dc:creator>Ng, Siu-Hung</dc:creator> <dc:creator>Schauenburg, Peter</dc:creator> <dcterms:issued>2010</dcterms:issued> <dc:date rdf:datatype="">2011-07-20T09:19:57Z</dc:date> </rdf:Description> </rdf:RDF>

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