Pierre Emmanuel Caprace - Groups with irreducibly unfaithful subsets for unitary representations
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 22/12/2018

A subset F of a group G is called irreducibly faithful if G has an irreducible unitary representation whose kernel does not contain any non-trivial element of F. We say that G has  property
P(n)  if  every  subset  of  size  at  most n is  irreducibly  faithful.  By  a classical  result  of  Gelfand  and  Raikov,  every  group  has
P(1).  Walter  proved  that  every group has P(2). The goal of this talk, based on a joint work with Pierre de la Harpe, is to  provide,  for  each  positive  integer n,  a  purely  group  theoretic characterization  of  the countable groups satisfying P(n).