Orbit separation and stratification by isotropy classes of piezoelectricity tensors
Résumé
We explore an innovative method to compute separating invariants in a real G-variety V. A refinement of Seshadri slice Lemma enables us to decompose V into a union of stable subsets GZ1 ... GZr. It then reduces the problem to separating the orbits in the slices Zi for their normalizers Ni < G. This sequencing allows also to identify efficiently the isotropy class of any point. After the presentation of three types of Seshadri slices for representations of SO3(R), we apply the method to the space of piezoelectricity tensors Piez. It provides a separating set of low cardinality and a complete stratification of Piez by isotropy classes.
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