Irreducible representations of tree automorphism groups into Pontryagin spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908891833434112 |
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| author | Viola, Federico |
| author_facet | Viola, Federico |
| contents | Let G = Aut(T) be the automorphism group of a regular tree T. We study continuous irreducible representations of G that preserve a continuous strongly nondegenerate sesquilinear form of finite index on a Hilbert space. These are already classified for index 0 (unitary case) and for index 1. We show that there are no more representations for index > 1, which completes the classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible representations of tree automorphism groups into Pontryagin spaces Viola, Federico Group Theory Metric Geometry Representation Theory Let G = Aut(T) be the automorphism group of a regular tree T. We study continuous irreducible representations of G that preserve a continuous strongly nondegenerate sesquilinear form of finite index on a Hilbert space. These are already classified for index 0 (unitary case) and for index 1. We show that there are no more representations for index > 1, which completes the classification. |
| title | Irreducible representations of tree automorphism groups into Pontryagin spaces |
| topic | Group Theory Metric Geometry Representation Theory |
| url | https://arxiv.org/abs/2508.02367 |