What type of study is this?

This is a Quantitative Study study.

October 13, 2025Open Access

Orbit recovery from invariants of low degree in representations of finite groups

Key Points

Invariants of degree up to three effectively separate generic orbits in finite group representations, demonstrating new insights.
The study answers a significant question posed by Bandeira et al. in 2023 regarding the representation theory of finite groups.
A discussion on the implications for subregular representations of dihedral and symmetric groups is included, expanding the theoretical framework.
These advancements could enhance applications in fields like neural networks and cryo-electron microscopy.

Abstract

Motivated by applications to equivariant neural networks and cryo-electron microscopy we consider the problem of recovering the generic orbit in a representation of a finite group from invariants of low degree. The main result proved here is that invariants of degree at most three separate generic orbits in the regular representation of a finite group defined over any infinite field. This answers a question posed in a 2023 ACHA paper of Bandeira et. al. We also discuss this problem for subregular representations of the dihedral and symmetric groups.

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Cite This Study

Edidin et al. (Sun,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d1889d https://doi.org/https://doi.org/10.48550/arxiv.2503.00009

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