Groups acting on rooted trees and representations on the boundary

Every action of a group on a rooted tree induces an action on the boundary of the tree. This action yields various representations of the group on spaces of functions on the boundary. In this talk we discuss the structure of such representations. After reviewing of the basic concepts, we will introduce locally 2-transitive actions on trees and give examples of such actions. It will be discussed how this property gives rise to an explicit decomposition of the boundary representation into irreducible constituents.