Title: Character Rigidity for Lattices and Commensurators
Speaker: Darren Creutz
Characters on groups (positive definite conjugation-invariant functions) arise naturally both from probability-preserving actions (the measure of the set of fixed points) and unitary representations on finite factors (the trace). I will present joint work with J. Peterson showing that for lattices in semisimple groups (and their commensurators) the only characters are the trivial character and the weakly almost periodic characters (arising from finite-dimensional representations).Date: Wednesday, December 4, 2013
This amounts to an operator algebraic superrigidity theorem for such lattices--any homomorphism from a lattice into the unitary group of a finite factor is either precompact or extends to a homomorphism of the group von Neumann algebra, answering a question of Connes. Consequently, any nonatomic probability-preserving action of such a lattice is essentially free.