Complex hyperbolic representations of groups and Möbius transformations at infinity.

This talk will focus on isometric representations in hyperbolic spaces of infinite dimensions. Pierre Py and Nicolas Monod have shown that these exhibit behaviour that is radically different from that of representations in finite dimensions (e.g. for the groups PO(1,n) and PU(1,n).

In the first half, we will explain some general principles as well as techniques introduced by the aforementioned authors that allow the deformation of representations through the study and manipulation of orbit maps.

In the second part, we will study an isometric representation via the action by Möbius transformations induced on the limit set. Using this framework, it will be possible to describe new representations and state some classification results.