Irreducible representations of tree automorphism groups into Pontryagin spaces
Group Theory
2026-03-18 v2 Metric Geometry
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2508.02367,
title = {Irreducible representations of tree automorphism groups into Pontryagin spaces},
author = {Federico Viola},
journal= {arXiv preprint arXiv:2508.02367},
year = {2026}
}
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37 pages