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arXiv · 2405.15391

Representation theory of the group of automorphisms of a finite rooted tree

Fabio Scarabotti
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Abstract

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions, a natural generalization of set compositions but with new features and more complexity. These combinatorial structures lead to a family of permutation representations which have the same parametrization of the irreducible representations. Our trees are not necessarily spherically homogeneous and our approach is coordinate free.

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BibTeXRIS

Fabio Scarabotti. 2024-05-24. Representation theory of the group of automorphisms of a finite rooted tree. https://arxiv.org/abs/2405.15391

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