Integral modular data and congruences
Michael Cuntz
Universität Kaiserslautern Postfach 3049 67653 Kaiserslautern Germany
DOI: 10.1007/s10801-008-0139-y
Abstract
We 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 \Bbb Z/2\Bbb 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.
Pages: 357–387
Keywords: keywords modular data; fusion algebra; quantum double; Fourier matrix; modular group
Full Text: PDF
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