Henry Tucker

University of California, San Diego | UCSD · Department of Mathematics

We give formulas for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semi-simple spherical tensor category $\mathcal{C}$. In particular, this implies for a finite depth planar algebra, the entire collection of rotation eigenvalues can be computed from the fusion rules and t...

We give formulae for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semisimple spherical tensor category $\mathcal{C}$. In particular, this implies that the entire collection of rotation eigenvalues for a fusion category can be computed from the fusion rules and the traces...

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 non-invertible simple object: near groups, those fusion categories...

We prove that integral modular categories of Frobenius-Perron dimension $pq^5$ are group-theoretical, where $p,q$ are distinct prime numbers. Combining this with previous results in the literature, integral modular categories of Frobenius-Perron dimension $pq^i$, $0\leq i\leq 5$, are group-theoretical. We also prove a sufficient and necessary condi...