An explicit construction of the K-finite vectors in the discrete series for an isotropic semisimple symmetric space
Analyse harmonique sur les groupes de Lie et les espaces symétriques (Actes du colloque du Kleebach, 20-24 mai 1983), Mémoires de la Société Mathématique de France, Série 2, no. 15 (1984), pp. 157-199.
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     author = {Flensted-Jensen, Mogens and Okamoto, Kiyosato},
     title = {An explicit construction of the {K-finite} vectors in the discrete series for an isotropic semisimple symmetric space},
     booktitle = {Analyse harmonique sur les groupes de Lie et les espaces sym\'etriques (Actes du colloque du Kleebach, 20-24 mai 1983)},
     editor = {Duflo, Michel and Eymard, Pierre and Schiffmann, G\'erard},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     pages = {157--199},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {15},
     year = {1984},
     doi = {10.24033/msmf.303},
     mrnumber = {87c:22025},
     zbl = {0563.22008},
     url = {http://archive.numdam.org/articles/10.24033/msmf.303/}
}
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Flensted-Jensen, Mogens; Okamoto, Kiyosato. An explicit construction of the K-finite vectors in the discrete series for an isotropic semisimple symmetric space, dans Analyse harmonique sur les groupes de Lie et les espaces symétriques (Actes du colloque du Kleebach, 20-24 mai 1983), Mémoires de la Société Mathématique de France, Série 2, no. 15 (1984), pp. 157-199. doi : 10.24033/msmf.303. http://archive.numdam.org/articles/10.24033/msmf.303/

[1] Berger,M., Les espaces symétriques non compacts. Ann. Sci. École Norm. Sup., 74 (1957), 85-177. | Numdam | MR | Zbl

[2] Faraut, J., Distributions sphériques sur les espaces hyperboliques. J. Math. pures et appl. 58 (1979), 369-444. | MR | Zbl

[3] Flensted-Jensen, M., Discrete series for semisimple symmetric spaces. Ann. of Math. 111 (1980), 253-311. | MR | Zbl

[4] Flensted-Jensen, M., Harmonic analysis on semisimple symmetric spaces. A method of duality. To appear in the proceedings of the Special Year in Lie Groups. University of Maryland, 1982-1983. (Springer Lecture Notes in Mathematics).

[5] Harish-Chandra Spherical functions on a semisimple Lie group I and II. Amer. J. Math. 80 (1958), 241-310 and 553-613. | MR | Zbl

[6] Helgason, S., A duality for symmetric spaces with applications to group representations. Adv. Math. 5 (1970), 1-154. | MR | Zbl

[7] Helgason, S., A duality for symmetric spaces with applications to group representations II. Differential equations and eigenspace representations. Adv. Math. 22 (1976), 187-219. | MR | Zbl

[8] Helgason, S., Differential geometry, Lie groups and symmetric spaces. Academic Press, New York-San Francisco-London 1978. | Zbl

[9] Helgason, S., Groups and geometric analysis I. To appear Academic Press. | Zbl

[10] Kashiwara, M., Kowata, A., Minemura, K., Okamoto, K., Oshima, T. and Tanaka, M., Eigenfunctions of invariant differential operators on a symmetric space. Ann. of Math., 107 (1978), 1-39. | MR | Zbl

[11] Kosters, M.T., Spherical distributions on rank one symmetric spaces. Thesis, University of Leiden, 1983.

[12] Loos, O., Symmetric spaces. I, II. New York-Amsterdam, W.A. Benjamin, Inc., 1969. | MR | Zbl

[13] Matsuki, T., The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan 31 (1979), 331-357. | MR | Zbl

[14] Oshima, T. and Matsuki, T., A description of discrete series for semisimple symmetric spaces. Preprint 1983.

[15] Oshima, T. and Sekiguchi, J. : Eigenspaces of invariant differential operators on an affine symmetric space, Inventiones Math. 57 (1980), 1-81. | EuDML | MR | Zbl

[16] Schlichtkrull, H., The Langlands parameters of Flensted-Jensen's discrete series for semisimple symmetrics spaces, J. Func. Anal. 50 (1983), 133-150. | MR | Zbl

[17] Schlichtkrull, H., Applications of hyperfunction Theory to representations of semisimple Lie groups. Rapport 2 a-b, Dept. of Math., University of Copenhagen, April 1983.

[18] Strichartz, R.S., Harmonic analysis on hyperboloids. J. Funct. Anal. 12 (1973), 341-383. | MR | Zbl

[19] Takahashi, R., Quelques résultats sur l'Analyse Harmonique dans l'espace symétrique non compact de rang 1 du type exceptionnel. In : Lecture notes in Mathematics vol. 793, 511-567. Springer Verlag, Berlin, 1979. | MR | Zbl

[20] Vogan, D., Algebraic structure of irreductible representations of semisimple Lie groups. Ann. of Math. 109 (1979), 1-60. | MR | Zbl

[21] Speh, B. and Vogan, D., Reducibility of generalized principal series representations. Acta Math. 145 (1980), 227-299. | MR | Zbl

[22] Wolf, J.A., Spaces of constant curvature. McGraw-Hill, New York, 1967. | MR | Zbl

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