Representation theory of the group of automorphisms of a finite rooted tree
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910910054924288 |
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| author | Scarabotti, Fabio |
| author_facet | Scarabotti, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representation theory of the group of automorphisms of a finite rooted tree Scarabotti, Fabio Representation Theory 20C15, 05E10, 20B25, 20C30 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. |
| title | Representation theory of the group of automorphisms of a finite rooted tree |
| topic | Representation Theory 20C15, 05E10, 20B25, 20C30 |
| url | https://arxiv.org/abs/2405.15391 |