A note on irreducible representations of profinite nilpotent groups (Q1113280)

Let G be a profinite nilpotent group. We show that the complex continuous finite dimensional irreducible representations of G can be parameterized by certain linear \((=\) one dimensional) characters of G. Therefore, if G is the Galois group of the maximal nilpotent extension of a local or global number field k class field theory implies that the representations in question are given by certain continuous linear characters of the multiplicative group of k resp. the idele class group of k.