Near-group fusion categories and their doubles

Source: arXiv

ABSTRACT 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 E6 and affine-D5 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

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