David Jaklitsch: The braided monoidal structure of tube algebra representations

Abstract: Ocneanu's tube algebra plays a central role in lattice models of Levin-Wen type, where topological excitations are given by irreducible representations. The purpose of the talk is to report on our recent results explicitly describing the tensor product of tube algebra representations and the braiding. The well-known linear equivalence between tube algebra representations and the Drinfeld center category is (by means of this structure) upgraded to a braided monoidal equivalence. This is joint work with Makoto Yamashita.