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.
G-Invariant Representations using Coorbits: Injectivity Properties
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on subsets of sorted coorbits with respect to selected window vectors. We derive conditions under which such embeddings are injective, using techniques from semi-algebraic analysis. These results are then applied to the specific case of planar rotation invariance.
fields
math.RT 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.