Phase retrieval for nilpotent groups
Abstract
We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected connected Lie groups, and for finite groups. We prove by induction that in the Lie group case, all irreducible representations do phase retrieval. For the finite group case, we mostly focus on -groups. Here our main result states that every irreducible representation of an arbitrary -group with exponent and size does phase retrieval. Despite the fundamental differences between the two settings, our inductive proof methods are remarkably similar.
Cite
@article{arxiv.2201.08654,
title = {Phase retrieval for nilpotent groups},
author = {Hartmut Führ and Vignon Oussa},
journal= {arXiv preprint arXiv:2201.08654},
year = {2023}
}
Comments
Revised version, correcting some insufficient assumptions made in the previous version. In particular, the general theorem about $p$-groups is only established for $p$-groups of exponent $p$