The center of the extended Haagerup subfactor has 22 simple objects

Abstract

We explain a technique for discovering the number of simple objects in Z(), the center of a fusion category , as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring K() and the dimension function K. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165.] to compute the full modular data