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- W2021000789 abstract "We show that the vector space of fixed valence Killing tensors on a space of constant curvature is naturally isomorphic to a certain highest weight, irreducible representation of the general linear group. The isomorphism is equivariant in the sense that the natural action of the isometry group corresponds to the restriction of the linear action to the appropriate subgroup. As an application, we deduce the Delong–Takeuchi–Thompson formula on the dimension of the vector space of Killing tensors from the classical Weyl dimension formula. To cite this article: R.G. McLenaghan et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). Nous démontrons que l'espace des tenseurs de Killing d'un ordre donné est naturellement isomorphe à une représentation irréductible de plus haut poids du groupe linéaire. L'isomorphisme est équivariant ; les transformations par isométries correspondent à l'inclusion du groupe des isométries comme un sous-groupe particulier du groupe linéaire. Comme application de cet isomorphisme nous obtenons la formule de Delong–Takeuchi–Thompson sur la dimension de l'espace des tenseurs de Killing à partir de la formule classique de dimension de Weyl. Pour citer cet article : R.G. McLenaghan et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004)." @default.
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- W2021000789 date "2004-11-01" @default.
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- W2021000789 title "Killing tensors as irreducible representations of the general linear group" @default.
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