Title: Constructing Haagerup-Izumi fusion categories using special functions
Abstract: Haagerup-Izumi fusion categories arose from Izumi's work on endomorphisms of Cuntz algebras and subfactors, and are among the best-known examples of exotic fusion categories. Although their fusion rules are relatively simple, constructing categories that realize them has been a difficult problem, with only a few examples previously known. In joint work with Terry Gannon and Andrew Schopieray, we give a uniform construction of Haagerup-Izumi fusion categories associated with Z/NZ for every odd N. The key ingredient is the Barnes double-sine function, whose special values provide explicit solutions to the polynomial equations arising from Izumi's construction. I will explain the main ideas behind this construction, discuss unitarity, and describe modular data of their Drinfeld centers, which are modular tensor categories