Rooted trees and iterated wreath products of cyclic groups

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...

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Published inAdvances in applied mathematics Vol. 33; no. 3; pp. 531 - 547
Main Authors Orellana, R.C., Orrison, M.E., Rockmore, D.N.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.10.2004
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Partially ordered set
Irreducible representation
Cyclic group
Applied mathematics
Decomposition method
Combinatorics
Rooted tree
Bratteli diagram
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2003.12.001