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

TL;DR

This paper proves that all parabolically induced unitary representations of the universal group U(F)^+ have matrix coefficients that vanish at infinity, extending known results from 2-transitive cases to primitive F.

Contribution

It introduces a new strategy to show that all such representations of U(F)^+ are C_0, generalizing previous results for 2-transitive F.

Findings

All parabolically induced representations of U(F)^+ are C_0.

The result extends to primitive F, broadening the class of groups with this property.

The approach generalizes known cases for 2-transitive F.

Abstract

By employing a new strategy we prove that all parabolically induced unitary representations of the Burger-Mozes universal group U(F)^+, with F being primitive, have all their matrix coefficients vanishing at infinity. This generalizes the same well-known result for the universal group U(F)^+, when F is 2-transitive.