Operator algebra seminar

Speaker: David Kerr (Texas A&M)

Title: Quantum groups, property (T), and weak mixing

Abstract: For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This generalizes results of Bekka–Valette (from the group setting) and Daws–Skalski–Viselter (from the setting of low dual) and is established using completely different methods. As a consequence we obtain quantum group versions of characterizations of property (T) of Kerr–Pichot in terms of the Baire category theory of weak mixing representations and of Connes–Weiss in term of the prevalence of strongly ergodic actions. This is joint work with Michael Brannan.