Benabdallah, Abdel-Ilah L’opérateur de Casimir de \(SL(3,{\mathbb{R}})\). (English) Zbl 0543.22006 Ann. Sci. Éc. Norm. Supér. (4) 17, 269-291 (1984). 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 Cited in 1 ReviewCited in 1 Document MSC: 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 Keywords:Casimir operator; fundamental solution PDF BibTeX XML Cite \textit{A.-I. Benabdallah}, Ann. Sci. Éc. Norm. Supér. (4) 17, 269--291 (1984; Zbl 0543.22006) Full Text: DOI Numdam EuDML OpenURL References: [1] S. HELGASON , Amer. Math. Soc., 14, 1972 . MR 47 #5179 [2] S. LANG , SL2 (R), Addison Wesley, New York, 1975 . [3] L. SCHWARTZ , Théorie des distributions , Hermann, Paris, 1966 . MR 35 #730 | Zbl 0149.09501 · Zbl 0149.09501 [4] P. METHEE , Sur les distributions invariantes dans le groupe des rotations de Lorentz (Commentarii Math. Helvetici, vol. 28, 1954 , p. 225-269). MR 16,255c | Zbl 0055.34101 · Zbl 0055.34101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.