Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

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

paper · doi:10.48550/arxiv.1409.0604

Abstract

Consider the generalized iterated wreath product S_r1\wr … \wr S_rk of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.

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