Radu groups acting on trees are CCR

Abstract

We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting $2$-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia's CCR conjecture on trees for $(d_0,d_1)$-semi-regular trees such that $d_0,d_1\in \Theta$, where $\Theta$ is an asymptotically dense set of positive integers.

46 pages, 8 figures

References in corpus (3)

• A product for permutation groups and topological groups
• A classification theorem for boundary 2-transitive automorphism groups of trees
• A note on type I groups acting on d-regular trees