Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Mee Seong Im; Angela Wu

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arXiv · 1409.0603

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Mee Seong Im·Angela Wu

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Abstract

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.

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BibTeX RIS

Mee Seong Im, Angela Wu. 2014-09-02. Generalized iterated wreath products of cyclic groups and rooted trees correspondence. https://arxiv.org/abs/1409.0603

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