Tube algebra of group-type subfactors

Abstract

We describe the tube algebra and its representations in the cases of diagonal and Bisch–Haagerup subfactors possibly with a scalar [Formula: see text]-cocycle obstruction. We show that these categories are additively equivalent to the direct product over conjugacy classes of representation category of a centralizer subgroup (corresponding to the conjugacy class) twisted by a scalar [Formula: see text]-cocycle obtained from the [Formula: see text]-cocycle obstruction.