One generic complex orbit determines a finite linear symmetry group up to isomorphism; two generic real orbits suffice, and concrete recovery needs an orbit count governed by representation multiplicities.
Injectivity, stability, and positive definiteness of max filtering
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abstract
Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclidean space, and when G is finite, we estimate the map's distortion of the quotient metric. We also characterize when max filtering is a positive definite kernel.
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2024 1verdicts
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Recovering a group from few orbits
One generic complex orbit determines a finite linear symmetry group up to isomorphism; two generic real orbits suffice, and concrete recovery needs an orbit count governed by representation multiplicities.