| Tim de Laat - Universität Münster,
|Gelfand pairs, spherical functions and exotic group C*-algebras
|14:00 à 15:00
|For a non-amenable group G, there can be many group C*-algebras that lie naturally between the universal and the reduced C*-algebra of G. These are called exotic group C*-algebras. Let G be a simple Lie group or an appropriate locally compact group acting on a tree. I will explain how the L^p-integrability properties of different spherical functions on G (relative to a maximal compact subgroup) can be used to distinguish between different exotic group C*-algebras. This recovers results of Samei and Wiersma. Additionally, I will explain that under certain natural assumptions, the aforementioned exotic group C*-algebras are the only ones coming from G-invariant ideals in the Fourier-Stieltjes algebra of G. This is based on joint work with Dennis Heinig and Timo Siebenand.