Clerc, Jean-Louis 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 J. Reine Angew. Math. 423, 47-71 (1991). 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) Cited in 1 ReviewCited in 3 Documents MSC: 17C10 Structure theory for Jordan algebras 17C36 Associated manifolds of Jordan algebras Keywords:invariant polynomials; Euclidean Jordan algebras; radial polynomials; representations; Stiefel harmonics; separation of variables; harmonic polynomials PDFBibTeX XMLCite \textit{J.-L. Clerc}, J. Reine Angew. Math. 423, 47--71 (1991; Zbl 0749.17042) Full Text: Crelle EuDML