Near-group fusion categories and their doubles

نویسندگان

David E. Evans

Terry Gannon

چکیده

A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the D (1) 5 and E6 subfactors, though there are infinitely many others. We classify the near-group fusion categories, and compute their doubles and the modular data relevant to conformal field theory. Among other things, we explicitly construct over 40 new finite depth subfactors, with Jones index ranging from around 6.85 to around 14.93. We expect all of these doubles to be realised by rational conformal field theories. keywords: near-group fusion category; subfactors; tube algebra; modular data

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Article history: Received 10 March 2016 Accepted 17 January 2017 Available online xxxx Communicated by Dan Voiculescu

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