Ng and Schauenburg generalized higher Frobenius–Schur indicators to pivotal fusion
categories and showed that these indicators may be computed utilizing the modular
data of the Drinfel’d center of the given category. We consider two classes of fusion
categories generated by a single noninvertible simple object: near groups, those fusion
categories with one noninvertible object, and Haagerup–Izumi categories, those with
one noninvertible object for every invertible object. Examples of both types
arise as representations of finite or quantum groups or as Jones standard
invariants of finite-depth Murray–von Neumann subfactors. We utilize the
computations of the tube algebras due to Izumi and to Evans and Gannon to
obtain formulae for the Frobenius–Schur indicators of objects in both of these
families.
