Constructing Haagerup-Izumi fusion categories using special functionsOberseminar Darstellungstheorie

by Harshit Yadav (MPI)

Friday Nov 6, 2026, 2:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Fusion categories generalize the representation categories of finite groups. Some categories, such as the Haagerup fusion category are exotic: no construction from groups or quantum groups is known. Izumi placed it in a family of Haagerup-Izumi categories, one for each abelian group G of odd order. He reduced their existence to polynomial equations in a single matrix, but solutions were known only for small groups. We give an explicit solution for every cyclic group Z/N of odd order, built using the Barnes-Shintani double sine function. We also compute the modular data of their Drinfeld centers, proving a conjecture of Evans and Gannon for cyclic groups. This is based on joint work with Terry Gannon and Andrew Schopieray.