UNITARY REPRESENTATIONS OF TOTALLY DISCONNECTED LOCALLY COMPACT GROUPS SATISFYING OLISHANSKII'S FACTORISATION

Inspired by Ol's ˇhanskii's work, we provide an axiomatic framework to describe certain irreducible unitary representations of non-discrete unimodular totally disconnected locally compact groups. We look at the applications to certain groups of automorphisms of locally finite trees and semi -regular right-angled buildings.