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

2025/02/16 by Edidin, Dan, Katz, Josh · 2 citations
#13A50 #94A12 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.00009

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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