Computing F-symbols for the center of a fusion category via tube algebras

Abstract: Applications of fusion categories often require the F-symbols to be known explicitly, for example, for constructing lattice models in physics. Although, in principle, these matrices can always be determined by solving the pentagon equation, this task is often difficult in practice since it corresponds to solving a vast system of coupled polynomial equations in a large number of variables. This is especially true if we are interested in the center of a fusion category, which typically has too many objects and multiplicities to allow for a direct calculation of the F-symbols. In this talk, I will discuss how one can construct the center (including the F-symbols) from a known fusion category using representation theory of the tube algebra of the category.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home