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We develop a symbolic computational approach to classifying lowrank modular fusion categories, up to finite ambiguity. By a generalized form of Ocneanu rigidity due to Etingof, Ostrik and Nikshych, it is enough to classify modular fusion algebras of a given rank–that is, to determine the possible Grothendieck rings with modular realizations. We use this… (More)

We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to YangBaxter operators in monoidal categories. The essential problem is to determine when a family of braid representations can be uniformly modelled upon a tensor power of a fixed vector space in such a way that the… (More)

- Seung-Moon Hong
- 2009

Abstract. It is known that every ribbon category with unimodality allows symmetrized 6j-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category E. We define the mirror conjugate symmetry of 6j-symbols instead and show that 6j-symbols of any unitary spherical… (More)

- Shawn X. Cui, Seung-Moon Hong, Zhenghan Wang
- Quantum Information Processing
- 2015

Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum… (More)

We classify pseudo-unitary modular categories of rank at most 5 under the assumption that some simple object is not isomorphic to its dual. Our approach uses Gröbner basis computations, and suggests a general computational procedure for classifying low-rank modular categories.

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