L’opérateur de Casimir de \(SL(3,{\mathbb{R}})\). (English) Zbl 0543.22006

Author’s abstract: ”Let \(G=SL(2,{\mathbb{R}})\) and \(\omega\) be its Casimir operator. We compute explicitly a fundamental solution of \(\omega\) and we prove that there is no central elementary solution. We characterize the image by \(\omega\) of the space of central and \(C^{\infty}\) maps defined on G.”
Reviewer: T.Jørgensen


22E30 Analysis on real and complex Lie groups
43A80 Analysis on other specific Lie groups
35A08 Fundamental solutions to PDEs
22E46 Semisimple Lie groups and their representations
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