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Representation of a Jordan algebra, invariant polynomials and Stiefel harmonics. (Représentation d’une algèbre de Jordan, polynômes invariants et harmoniques de Stiefel.) (French) Zbl 0749.17042
Representations of Euclidean (= formally real) Jordan algebras are studied and classified. When the representation satisfies a certain rank condition (called regularity) then the space \(E\) of the representation admits a “polar” decomposition. A characterization of the “radial” polynomials is obtained, which is related to Weyl’s first fundamental theorem of invariants. Stiefel harmonics are introduced and used to prove under appropriate conditions a “separation of variables” theorem for polynomials on \(E\). There are a few other results generalizing classical properties of the radial or harmonic polynomials.
Reviewer: J.-L.Clerc (Nancy)

MSC:
17C10 Structure theory for Jordan algebras
17C36 Associated manifolds of Jordan algebras
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