Rooted Trees and Iterated Wreath Products of Cyclic Groups

Authors

Rosa C. Orellana, Dartmouth College
Michael E. Orrison Jr., Harvey Mudd CollegeFollow
Daniel N. Rockmore, Dartmouth College

Document Type

Article

Department

Mathematics (HMC)

Publication Date

7-28-2004

Abstract

Let W_n,r denote the n-fold iterated wreath product of with itself. In this paper, we are interested in the tower of groups W_1,rW_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.

Rights Information

©2004 Elsevier

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Recommended Citation

Orellana, R.C., Orrison, M.E., and Rockmore, D. "Rooted trees and iterated wreath products of cyclic groups." Advances in Applied Mathematics 33 (2004), no. 3, 531-547. .