Characters of nilpotent groups

Abstract

The characters (extremal positive definite central functions) of discrete nilpotent groups are studied. The relationship between the set of characters of G and the primitive ideals of the group C-algebra C(G) is investigated. It is shown that for a large class of nilpotent groups these objects are in 1–1 correspondence. One proof of this exploits the fact that faithful characters of certain nilpotent groups vanish off the finite conjugacy class subgroup. An example is given where the latter property fails. Show more