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Inducing spherical representations of semi-simple Lie groups

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Rozprawy Matematyczne tom/nr w serii: 122 wydano: 1975
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Abstrakty
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Contents
Introduction............................................................................................................................................................................... 5
Chapter I. Preliminaries and notations....................................................................................................................... 8
    1. Manifolds—generalities................................................................................................. 8
    2. Representations............................................................................................................. 8
    3. Induced representations............................................................................................... 10
    4. Elements of structure theory of semi-simple Lie groups........................................ 11
    5. Homogoneous spaces of semi-simple Lie groups................................................ 12
    6. Measures on G and its homogeneous spaces........................................................ 13
    7. Invariant differential operators on homogeneous spaces...................................... 14
Chapter II. Spherical representations and spherical functions—General results..................................................... 15
Chapter III. Some representations in function spaces.................................................................................................... 19
Chapter IV. Conical representations and conical distributions...................................................................................... 27
Chapter V. Induced spherical representations................................................................................................................. 38
References............................................................................................................................................................................... 46
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 122
Liczba stron
47
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXXII
Daty
wydano
1975
Twórcy
Bibliografia
  • [1] A. Borel, Représentations de groupes localement compacts, Lecture Notes in Mathematics 270, Springer-Verlag 1972.
  • [2] P. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), pp. 97-205.
  • [3] I. M. Gelfand, Spherical functions on symmetric spaces (in Russian), Dokl. Akad. Nani SSSR 70 (1960), pp. 5-8.
  • [4] I. M. Gelfand and M. A. Naimark, Unitary representations of classical groups (in Russian), Tr. Mat. Inst. Steklova AN SSSR 36 (1950).
  • [5] S. G. Gindikin and F. I. Karpelevic, Plancherel measure of Riemannian symmetric spaces of non-positive curvature (in Russian), Dokl. Akad. Nauk SSSR 145 (1962), pp. 252-255.
  • [6] R. Godement, A theory of spherical functions I, Trans. Amer. Math. Soc. 73 (1952), pp. 496-556.
  • [7] R. Goodman, Analytic and entire vectors for representations of Lie groups, Trans. Amer. Math, Soc. 143 (1969), pp. 55-76.
  • [8] Harish-Chandra, Representations of semi-simple Lie groups I, Trans. Amor. Math. Soc. 75 (1953), pp. 185-243.
  • [9] Harish-Chandra, Representations of semi-simple Lie groups II, ibidem 70 (1964), pp. 26-65.
  • [10] Harish-Chandra, Spherical functions on a semi-simple Lie group I, Amer. J. Math. 80 (1958), pp. 241-310.
  • [11] Harish-Chandra, Spherical functions on a semi-simple Lie group II, ibidem 803 (1958), pp. 553-613.
  • [12] S. Helgason, Differential geometry and symmetric spaces, New York 1962.
  • [13] S. Helgason, Duality and Radon transform for symmetric spaces, Amer. J. Math. 85 (1963), pp. 667-692.
  • [14] S. Helgason, Lie groups and symmetric spaces, in Battelle Rencontres ed. by C. M. De Witt and J. A. Wheeler, pp. 1-71, Princeton 1968.
  • [15] S. Helgason, A duality for symmetric spaces with applications to group representations, Adv. in Math. 5 (1970), pp. 1-154.
  • [16] A. W. Knapp and E. M. Stein, Existence of complementary series, Problems in Analysis, Symposium in Honor of Salomon Bochner, Princeton 1970.
  • [17] A. W. Knapp and E. M. Stein, Intertwining operators for semi-simple Lie groups, Ann. of Math. 93 (1971), pp. 489-578.
  • [18] B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Soc. 75 (1969), pp. 627-649.
  • [19] R. A. Kunze and E. M. Stein, Uniformly hounded representations III, Amer. J. Math. 89 (1967), pp. 386-442.
  • [20] G. W. Mackey, Infinite-dimensional group representations, Bull. Amer. Math. Soc. 69 (1963), pp. 628-686.
  • [21] K. Maurin, General eigenfunction expansions and unitary representations of topological groups, Warszawa 1968.
  • [22] W. Parthasarathy, W. Ranga Rao, and W. Varadarajan, Representations of complex semi-simple Lie groups and Lie algebras, Ann. of Math. 85 (1967), pp. 383-429.
  • [23] N. Skovhus Poulsen, On $C^∞$-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal. 9 (1972), pp. 87-120.
  • [24] Gr. Schiffman, Sur les intégrales d'entrelacement de K. A. Kunze et E. M. Stein (thèse sc. math.), Bull. Soc. Math. France 99 (1971), pp. 3-72.
  • [25] T. Sherman, A weight theory for unitary representations, Canad. J. Math. 18 (1966), pp. 159-168.
  • [26] E. M. Stein, Analytic continuation of group representations, Adv. in Math. 4, pp. 172-207.
  • [27] A. Strasburger and A. Wawrzyńczyk, Automorphic forms for conical representations, Bull. Acad. Pol. Sci., Sér. sci. math., astr., phys. 20 (1972), pp. 921-927.
  • [28] G. Warner, Harmonic analysis on semi-simple Lie groups I, Springer-Verlag 1972.
  • [29] A. Wawrzyńczyk, A duality in the theory of group representations. Studia Math. 36 (1970), pp. 227-257.
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