Irreducible representations of tree automorphism groups into Pontryagin spaces

Federico Viola

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arXiv · 2508.02367

Irreducible representations of tree automorphism groups into Pontryagin spaces

Federico Viola

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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.

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Federico Viola. 2025-08-04. Irreducible representations of tree automorphism groups into Pontryagin spaces. https://arxiv.org/abs/2508.02367

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