Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$

Abstract

We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.