Rooted trees and iterated wreath products of cyclic groups

Abstract

Let W n, r denote the n-fold iterated wreath product of Z/r Z with itself. In this paper, we are interested in the tower of groups W 1, r ⊂ W 2, r ⊂⋯. We show that the irreducible representations of W n, r are indexed by a set of labeled rooted trees. By adding a partial order on this set of rooted trees, we obtain the Bratteli diagram for this tower of groups. In particular, we give the branching rules. This approach yields combinatorial rules for the decomposition of restricted and induced representations.