Harmonic analysis on semisimple symmetric spaces a method of duality

  • Mogens Flensted-Jensen
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1077)


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  1. [1]
    Berger, M., Les espaces symétriques non compacts. Ann. Sci. Ecole Norm. Sup., 74 (1957), 85–177.MathSciNetMATHGoogle Scholar
  2. [2]
    Clozel, L., Changement de base pour les représentations tempérées des groupes réductive réels. Ann. Sc. E.N.S. (4), 15 (1982), 45–115.MathSciNetMATHGoogle Scholar
  3. [3]
    Dixmier, J., Algebras Enveloppantes, Gauthier-Villars, Paris, 1974.MATHGoogle Scholar
  4. [4]
    Enright, T.J., Varadarajan, V.S., On an infinitesimal characterization of the discrete series. Ann. of Math., 102 (1975), 1–15.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Faraut, J., Distributions sphériques sur les espaces hyperbolic. J.Math. pures et appl. 58 (1979), 369–444.MathSciNetMATHGoogle Scholar
  6. [6]
    Flensted-Jensen, M., Spherical functions on rank one symmetric spaces and generalizations. Proceedings of symposia in pure mathematics, vol. XXVI, (Amer. Math. Soc. 1973), 339–342.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Flensted-Jensen, M., Spherical functions on a real semisimple Lie group. A method of reduction to the complex case. J. Funct. Anal. 30 (1978), 106–146.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Flensted-Jensen, M., Discrete series for semisimple symmetric spaces. Ann. of Math. 111 (1980), 253–311.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Flensted-Jensen, M., K-finite joint eigenfunctions of U(g)K on a non-Riemannian semisimple symmetric space G/H. In: Non commutative harmonic analysis and Lie groups, Proceedings, Marseille-Luminy 1980, ed. Carmona, J. and Vergne, M..Lecture Notes in Math. 880 (1981) 91–101.CrossRefMATHGoogle Scholar
  10. [10]
    Harish-Chandra, Representations of a semisimple Lie group on a Banach space, I. Trans. Amer. Math. Soc. 75 (1953), 185–243.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Harish-Chandra, Spherical functions on a semisimple Lie group I and II. Amer. J. Math. 80 (1958), 241–310 and 553–613.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Harish-Chandra, Discrete series for semisimple Lie groups, I, II. Acta Math. 113 (1965), 241–318, 116 (1966), 1–111.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    Harish-Chandra, Harmonic analysis on semisimple Lie groups. Bull. Amer. Math. Soc. 78 (1970), 529–551.MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Helgason, S. Differential geometry and symmetric spaces. Academic Press, New York 1962.MATHGoogle Scholar
  15. [15]
    Helgason, S., Fundamental solutions of invariant differential operators on symmetric spaces. Amer. J. Math. 86 (1964), 565–601.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Helgason, S., A duality for symmetric spaces with applications to group representations. Adv. Math. 5 (1970), 1–154.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Helgason, S., Eigenspaces of the Laplacian; integral representations and irreducibility. J. Functional Analysis 17 (1974), 328–353.MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    Helgason. S., A duality for symmetric spaces with applications to group representations II. Differential equations and eigenspace representations. Adv. Math. 22 (1976), 187–219.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    Helgason, S., Some results on eigenfunctions on symmetric spaces and eigenspace representations. Math. Scand. 41 (1977), 79–89.MathSciNetMATHGoogle Scholar
  20. [20]
    Helgason, S., Differential geometry, Lie groups and symmetric spaces. Academic Press, New York-San Francisco-London 1978.MATHGoogle Scholar
  21. [21]
    Helgason, S., Groups and geometric analysis I. To appear Academic Press.Google Scholar
  22. [22]
    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.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    Kengmana, T., Characters of the discrete series for pseudo-Riemannian symmetric spaces. Preprint, Harvard University, 1983.Google Scholar
  24. [24]
    Kosters, M.T., Spherical distributions on rank one symmetric spaces. Thesis, University of Leiden, 1983.Google Scholar
  25. [25]
    Knapp, T., Minimal K-type formula. Proceedings of the 1982-Marseille-Luminy Conference.Google Scholar
  26. [26]
    Loos, O., Symmetric spaces, I: General theory. New York-Amsterdam, W.A. Benjamin, Inc., 1969.MATHGoogle Scholar
  27. [27]
    Matsuki, T., The orbits of affine symmetric spaces under the action of minimal parabolic subgroups, J. Math. Soc. Japan 31 (1979), 331–357.MathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    Mostow, G.D., On covariant fiberings of Klein spaces. Amer. J. Math. 77 (1955), 247–278.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    Olafsson, G., Die Langlands-parameter für die Flensted-Jensensche Fundamentale Reihe. To appear.Google Scholar
  30. [30]
    Oshima, T., Poisson transformation of affine symmetric spaces. Proc. Jap. Acad. Ser. A 55 (1979), 323–327.MathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    Oshima, T., Fourier analysis on semisimple symmetric spaces. In: Non commutative harmonic analysis and Lie groups. Proceedings, Marseille-Luminy 1980, ed. Carmona, J. and Vergne, M. Lecture Notes in Math. 880, (1981), 357–369.CrossRefMATHGoogle Scholar
  32. [32]
    Oshima, T. and Matsuki, T., A complete description of discrete series for semisimple symmetric spaces. Preprint.Google Scholar
  33. [33]
    Oshima, T. and Sekiguchi, J.: Eigenspaces of invariant differential operators on an affine symmetric space, Inventiones Math. 57 (1980), 1–81.MathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    Rossmann, W., The structure of semisimple symmetric spaces. Can. J. Math. 31 (1979), 157–180.MathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    Schlichtkrull, H., The Langlands parameters of Flensted-Jensen's discrete series for semisimple symmetric spaces, J. Func. Anal. 50 (1983), 133–150.MathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    Schlichtkrull, H., A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group, Invent. Math. 68 (1982), 497–516.MathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    Schlichtkrull, H., Applications of hyperfunction Theory to representations of semisimple Lie groups. Rapport 2 a-b, Dept. of Math., University of Copenhagen, April 1983.Google Scholar
  38. [38]
    Schlichtkrull, H., One dimensional K-types in finite dimensional representations of semisimple Lie groups. to appear Math. Scand.Google Scholar
  39. [39]
    Strichartz, R.S., Harmonic analysis on hyperboloids. J. Funct. Anal. 12 (1973), 341–383.MathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    Vogan, D., Algebraic structure of irreducible representations of semisimple Lie groups. Ann. of Math. 109 (1979), 1–60.MathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    Wolf, J.A., Spaces of constant curvature. McGraw-Hill, New York, 1967.MATHGoogle Scholar
  42. [42]
    Wolf, J.A., Fineteness of orbit structure for real flag manifolds. Geom. Dedicata 3 (1974), 377–384.CrossRefMATHGoogle Scholar
  43. [43]
    Warner, G., Harmonic analysis on semi-simple Lie groups I and II. New York-Heidelberg-Berlin, Springer-Verlag, 1972.CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Mogens Flensted-Jensen
    • 1
  1. 1.Dept. of Mathematics and StatisticsRoyal Veterinary- and Agricultural UniversityCopenhagenDenmark

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