Analysis Seminar: "Positive type functions on groupoids and property (T)"

Abstract: Positive type functions on groups are important objects in the representation theory for groups. A remarkable fact is that the weak* and compact convergence topologies coincide on the space of normalized positive type functions on groups. We present a slight generalization of this fact to normalized positive type functions on groupoids. This observation motivates a notion of property (T) for groupoids that extends group property (T). We present some equivalent formulations of this property and first consequences.

Host: Xiang Tang