Orbit recovery from invariants of low degree in representations of finite groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917940978253824 |
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| author | Edidin, Dan Katz, Josh |
| author_facet | Edidin, Dan Katz, Josh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbit recovery from invariants of low degree in representations of finite groups Edidin, Dan Katz, Josh Representation Theory Information Theory 94A12, 13A50 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. |
| title | Orbit recovery from invariants of low degree in representations of finite groups |
| topic | Representation Theory Information Theory 94A12, 13A50 |
| url | https://arxiv.org/abs/2503.00009 |