RESEARCH IN PAIRS
An Ergodic Theorem à la Bader-Muchnik for Higher Rank Lattices
March 28 – April 8, 2016
March 28 – April 8, 2016
|
The action of a lattice of a semisimple Lie group on its Poisson Furstenberg boundary is ergodic. The irreducibility of the associated quasiregular representation is a stronger statement which is also true. Our goal is to find even stronger ergodicity conditions.
We generalize a result of Bader and Muchnik (ergodicity of the quasiregular representation on the Poisson Furstenberg boundary), proved in rank 1 for uniform lattices, to all lattices (uniform or not) without restriction on the rank. The ergodicity of the quasiregular representation on the Poisson Furstenberg boundary implies its irreducibility. We will study the possible weak mixing of this representation. |
Participants
Adrien Boyer (Technion – Israel Institute of Technology) Gabriele Link (Karlsruhe Institute of Technology) Christophe Pittet (Aix-Marseille Université) Sponsor  |