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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.07348 |
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Table of Contents:
- Let $n\le 5$ be an integer, and let $Γ$ be a finite group. We prove that if $ρ, ρ': Γ\to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element of $SO(n)$. In the process, we prove that if $G \subset O(4)$ is a finite group, then exactly one of the following is true: the elements of $G$ have a common invariant $1$-dimensional subspace in $\mathbb{R}^4$; some element of $G$ has no invariant $1$-dimensional subspace; or $G$ is conjugate to a specific group $K \subset O(4)$ of order $16$.