Generalized iterated wreath products of cyclic groups and rooted trees correspondence

2014/09/02 by Im, Mee Seong, Wu, Angela
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.0603

Abstract

Consider the generalized iterated wreath product ℤ_r1\wr ℤ_r2\wr … \wr ℤ_rk where r_i ∈ 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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