Integral modular data and congruences

dc.creatorCuntz, Michael
dc.date2006-11-08
dc.date2008-06-03
dc.date.accessioned2026-07-07T09:42:17Z
dc.date.available2026-07-07T09:42:17Z
dc.descriptionWe compute all fusion algebras with symmetric rational $S$-matrix up to dimension 12. Only two of them may be used as $S$-matrices in a modular datum: the $S$-matrices of the quantum doubles of $\mathbb{Z}/2\mathbb{Z}$ and $S_3$. Almost all of them satisfy a certain congruence which has some interesting implications, for example for their degrees. We also give explicitly an infinite sequence of modular data with rational $S$- and $T$-matrices which are neither tensor products of smaller modular data nor $S$-matrices of quantum doubles of finite groups. For some sequences of finite groups (certain subdirect products of $S_3,D_4,Q_8,S_4$), we prove the rationality of the $S$-matrices of their quantum doubles.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0611233
dc.identifierhttp://arxiv.org/abs/math/0611233
dc.identifierdoi:10.1007/s10801-008-0139-y
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162125
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject81R05; 16S99; 19A49; 20C40
dc.titleIntegral modular data and congruences
dc.typetext

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