Title: Compact hypergroups from discrete subfactors
Speaker: Luca Giorgetti, Vanderbilt University and Roma Tor Vergata
Abstract: Subfactors coming from inclusions of Conformal (Quantum) Field Theories have a rich structure and are highly constrained by physical requirements. They are often irreducible, braided (and local when they come from local CFTs). They are equipped with a conditional expectation encoding the “gauge” symmetries of the inclusion and the index may well be infinite when one takes CFTs with infinitely many superselection sectors into account. An inclusion is furthermore called “discrete” when only finite-dimensional sectors appear. We show, at the level of a single subfactor and assuming discreteness, how to construct a compact hypergroup acting (as generalized gauge symmetries) via ucp maps on the subfactor. The conditional expectation is determined as the Haar average of the hypergroup action, and the smaller algebra as the fixed-point subalgebra. In the case of subfactors with depth two, this hypergroup turns out to be a compact group.
Joint work with M. Bischoff (Ohio University) and S. Del Vecchio (Leipzig Universität). Supported by EU MSCA fellowship n. 795151.
