Un analogue non archimédien d'un résultat de Haagerup et lien avec la propriété (T) renforcée

Abstract

Inspired by a preprint of Haagerup and failed attempts to prove the Baum–Connes conjecture, we study the approximation of the trivial function on $S{L}_3$ or $S{p}_4$ on a local non-archimedian field, by spherical functions with good Schur multiplier properties when restricted to the Borel subgroup, or its unipotent radical.