Separation of the orbits in representations of SO 2 and O 2 over R and C - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Separation of the orbits in representations of SO 2 and O 2 over R and C

Résumé

We provide a minimal set of invariant polynomials separating all the orbits for representations of SO2 and O2 over C and R. We obtain very small cardinalities by selecting only polynomials of support of bounded dimension. Altough they suffice for a lot of applications, the obtained separating sets are much smaller than the already kwnown generating set. We also remark that real separating set are smaller than the complex ones. We next stratify entirely the orbit space through the evaluation of the invariant polynomials.
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Dates et versions

hal-04656738 , version 1 (22-07-2024)

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  • HAL Id : hal-04656738 , version 1

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Evelyne Hubert, Martin Jalard. Separation of the orbits in representations of SO 2 and O 2 over R and C. 2024. ⟨hal-04656738⟩
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