Théorie de Mackey pour les groupes adéliques

Sliman, Mohamed Hachmi

Astérisque, no. 115 (1984) , 160 p.

MR Zbl

@book{AST_1984__115__1_0,
     author = {Sliman, Mohamed Hachmi},
     title = {Th\'eorie de {Mackey} pour les groupes ad\'eliques},
     series = {Ast\'erisque},
     year = {1984},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {115},
     mrnumber = {753874},
     zbl = {0552.22001},
     language = {fr},
     url = {https://www.numdam.org/item/AST_1984__115__1_0/}
}

TY  - BOOK
AU  - Sliman, Mohamed Hachmi
TI  - Théorie de Mackey pour les groupes adéliques
T3  - Astérisque
PY  - 1984
IS  - 115
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1984__115__1_0/
LA  - fr
ID  - AST_1984__115__1_0
ER  -

%0 Book
%A Sliman, Mohamed Hachmi
%T Théorie de Mackey pour les groupes adéliques
%S Astérisque
%D 1984
%N 115
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1984__115__1_0/
%G fr
%F AST_1984__115__1_0

Sliman, Mohamed Hachmi. Théorie de Mackey pour les groupes adéliques. Astérisque, no. 115 (1984), 160 p. https://www.numdam.org/item/AST_1984__115__1_0/

Bibliographie
Cité par

{ A.K.} L. Auslander, B. Kostant : Polarisations and unitary representations of solvable Lie groups. Inventiones Math. 14 (1971) p. 255-354. | MR | Zbl | EuDML | DOI

{A.M.} L. Auslander, C.C. Moore : Unitary representations of solvable Lie groups. Memoirs of the Amer. Math. Soc. 62 1966) | MR | Zbl

{Be} P. Bernat, N. Conze, M. Duflo, M. L. Nahas, M. Raïs, P. Renouard, M. Vergne. Représentations des groupes de Lie résolubles. Monographie de la Soc. Math. de France. Dunod. Paris (1972). | MR | Zbl

{Bern} I. N. Bernstein : All reductive groups are tame. Functional Analysis and applications 8 (1974) p. 91-93. | Zbl | DOI

{Bl} R. Blattner : Group extention representation and the structure space. Pacific Journal of Math. 15 (1965) p. 1101-1113. | MR | Zbl | DOI

{Bol} A. Borel : Linear algebraic groups. W.A. Benjamin, Inc. New-York (1969) | MR | Zbl

{Bo2} A. Borel. Groupes linéaires algébriques. Annals of Math. 1 (1956) p. 20-82. | MR | Zbl | DOI

{Bo3} : A. Borel Some finiteness properties of adele groups over number fields. I.H.E.S. n° 16(1963) p. 101-126. | Zbl | MR | EuDML | Numdam

{Bo4} A. Borel. Introduction aux groupes arithmétiques. Hermann. Paris. (1969). | MR | Zbl

{Bo5} : A. Borel Formes automorphes et séris de Dirichlet d'après R.P.Langlands. Séminaire Bourbaki (1974-75) n° 466. | MR | Zbl | EuDML | Numdam

{B.G} A. Borel, H. Garland : Laplacian and the discrete spectrum of an arithmetic group. Amer. Journal of Math. 105 (1983) p. 309-335. | MR | Zbl | DOI

{B.H} A. Borel, Harish-Chandra : Arithmetic subgroups of algebraic groups. Annals of Math. 75 (1962) p. 485-535. | MR | Zbl

{B.M} A. Borel, G. D. Mostow : On semi-simple automorphisms of Lie algebras. Annals of Math. 61 (1955) p. 389-405. | MR | Zbl | DOI

{B.T} A. Borel, J. Tits : Groupes réductifs. I.H.E.S. n° 27 (1965) p. 55-152. | MR | EuDML

{B..} A. Borel,... : Proceeding of symposia in pure Math. vol. IX. Amer. Math. Soc. Providence, Rhode Island (1966).

{Br} J. Brézin : Harmonic analysis on compact solvmanifold. Lecture Notes in Math. 602 (1977). | MR | Zbl

{Chal} Harish-Chandra : Harmonic analysis on reductive $p$ -adic groups. Lecture Notes in Math. 162 (1970). | Zbl

{Cha2} :Harish-Chandra Automorphic forms on semi-simple Lie groups. Lecture Notes in Math. 62 (1968). | MR | Zbl

{Cha3} : Harish-Chandra Representations of semi-simple Lie groups on a Banach space. Transactions of the Amer. Math. Soc. 75 (1953) p. 185-243. | MR | Zbl | DOI

{Che} C. Chevailey : Théorie des groupes de Lie. Tome II. Hermann. Paris. (1951). | MR | Zbl

{Co} H. Cohn : A second course in number theory. John Willy &sons, Inc. (1962). | MR | Zbl

{Dix1} J. Dixmier : Sur les représentations unitaires des groupes de Lie algébriques. Annales de l'institut de Fourrier 7 (1957) p. 315-328. | DOI | MR | Zbl | EuDML | Numdam

{Dix2} : J. Dixmier Les $ℂ^{*}$ -algèbres et leurs représentations. Gauthiers-Villars. Paris (1964). | MR | Zbl

{Dix3} J. Dixmier Algèbres enveloppantes. Gauthiers-Villars. Paris (1974). | MR | Zbl

{Dix4} J. Dixmier. Représentations induites holomorphes des groupes résolubles algébriques. Bulletins de la Soc. Math. de France. 94 (1966) p. 181-206. | DOI | MR | Zbl | EuDML | Numdam

{D.M.} J. Dixmier, P. Malliavin : Factorisations des fonctions et des vecteurs indéfiniment différentiables. Bulletins de la Soc. Math. de France 102 (1978) p. 305-330. | MR | Zbl

{Du1}M. Duflo : Caractères des groupes et des algèbres de Lie résolubles. Annales scientifiques de l'E.N.S. 4 (1970) p. 23-74. | MR | Zbl | EuDML | Numdam

{Du2} : M. Duflo : Sur les extensions des représentations irréductibles des groupes de Lie nilpotents. Annales scientifiques de l'E.N.S. 4 (1972) p. 71-120. | MR | Zbl | EuDML | Numdam

{Du3} : M. Duflo Théorie de Mackey pour les groupes de Lie algébriques. Acta-Mathematica 149 [1983) p. 153-213 | MR | Zbl | DOI

{Gelb1} S. Gelbart : Automorphic forms on adele groups. Annals of Math. studies Princeton university press 83 (1975). | MR | Zbl

{Gelb2} : S. Gelbart : Weil's representation and the spectrum of the metaplectic group. Lecture Notes in Math. 530 (1976). | MR | Zbl

{G. G.P.S.1} I. M. Gelfand, M. I. Graev, Pyatetskii-Shapiro Representations of adele groups. Soviet math. A.M.S. translations vol 5 n° 3(1964) p. 657-661. | Zbl | MR

{G.G.P.S.2}.I. M. Gelfand, M. I. Graev, Pyatetskii-Shapiro - Representation theory and automorphic forms. W.B. Saunders. Philadelphia. (1969) | Zbl | MR

{Gl} J. Glimm : Type I ℂ-algebra. Annals of math. 73 (1961) p. 572-612. | Zbl | MR | DOI

{Go1} R. Godement : A theory of spherical functions. Transaction of the Amer. Math. Soc. 73 (1952) p. 496-556 . | MR | Zbl | DOI

{Go2} : R. Godement Groupes linéaire algébriques sur un corps parfait. Séminaire Bourbaki (1960-61) n° 206. | MR | Zbl | EuDML | Numdam

{Ho1} R. Howe : Frobenius reciprocity for unipotent algebraic groups over ℚ. Amer. Journal of Math. 93 (1971) p. 163-172. | MR | Zbl | DOI

{Ho2} R. Howe : On character of Weil's representation. Transaction of the Amer. Math. Soc. 177 (1973) p. 287-298. | MR | Zbl

{Ho3} : R. Howe Topics in harmonic analysis on solvable algebraic groups. Pacific Journal of Math. 73 (1977) p. 383-435. | MR | Zbl | DOI

{Hu} J. Humphreys : Linear algebraic groups. Springer-Verlag. (1975). | MR | Zbl | DOI

{I.M} N. Iwahoriy H. Matsumoto : On some Bruhat decomposation. I.H.E.S. 25 (1965) p. 5-48. | Zbl | EuDML | Numdam

{J.L} H. Jacquet, R. P. Langlands : Automorphic forms on Gl(2). Lecture Notes in Math. 114 (1970). | MR | Zbl

{K1} A. A. Kirillov : Unitary representations of nilpotent Lie groups. Uspekhi Math. Nauk 106 (1962) p. 57-110. | MR | Zbl

{K2} A. A. Kirillov: Eléments de la théorie des représentations. Editions Mir Moscou (1974). | MR

{La1} R. P. Langlands : On the functional equations satisfied by Eisenstein series. Lecture Notes in Math. 544 (1976). | MR | Zbl

{La2} R. P. Langlands : Dimensions of spaces of automorphic forms. Proc. in symposium in pure math. IX A.M.S. Providence (1966) p. 253-257. | Zbl | MR | DOI

{L.P} G. Liony P. Perrin : Extensions des représentations des groupes unipotents $p$ -adiques. Lecture Notes in Math. 880 (1981) p. 337-356. | MR | Zbl

{Li} R. Lipsman : The C.C.R. property for algebraic groups. Preprint dep. of math. University of Maryland College Park (1973). | MR | Zbl

{Ma1} G. W. Mackey : Unitary representation of group extensions I. Acta Mathematica 99 (1958) p. 265-311. | MR | Zbl | DOI

{Ma2} G. W. Mackey : Induced representations of locally compact groups. Annals of Math. 58 (1953) p. 193-221. | Zbl | MR | DOI

{Ma3} G. W. Mackey : Induced representations of locally compact groups I. Annals of Math. 55 (1952) p. 101-139. | MR | Zbl | DOI

{Ma4} G. W. Mackey : The theory of unitary representation. Mimeographed notes. University of Chicago. Lectures in Math. (1956).

{Moo1} C. C. Moore : Extensions and low dimensional cohomology theory of locally compact groups. Transactions of the Amer. Math.Soc. 113 (1964) p. 40-86. | Zbl

{Moo2} C. C. Moore : Decomposition of unitary representations defined by discrete subgroups of nilpotent groups. Annals of Math. 82 (1965) p. 146-182. | MR | Zbl | DOI

{M.V1} H. Moscovici, A. Verona : Cocycle representations of solvable Lie groups. Math. Zeitchrift Springer Verlag (1978) p. 1-12. | MR | Zbl

{M.V2} H. Moscovici, A. Verona : Harmonically induced representations of nilpotent Lie groups. Inventiones Math. 48 (1978) p. 61-73. | MR | Zbl | EuDML | DOI

{Mos1} G. D. Mostow : Fully reducible subgroups of algebraic groups. Amer. Journal of Math. 78 (1956) p. 200-221. | MR | Zbl | DOI

{Mos2} G. D. Mostow : Homogenious spaces with finite invariant measure. Annals, of Math. 75 (1962) p. 17-37. | MR | Zbl | DOI

{Mos3}G. D. Mostow : Factor spaces of solvable groups. Annals of Math. 60 (1954) p. 1-27. | MR | Zbl | DOI

{Mos4}G. D. Mostow : Representative functions on discrete groups and solvable arithmetic subgroups. Amer. Journal of Math. 92 (1970) p. 1-31. | MR | Zbl | DOI

{M.T} G. W. Mostow, T. Tamagawa : On the compactness of arithmetically defined homogeneous spaces. Annals of Math. 76 (1962) p. 446-463. | MR | Zbl | DOI

{N} J. V. Neumann : On infinite direct product. Compositio Mathematica 6 (1938) p. 1-77. | MR | Zbl | JFM | EuDML | Numdam

{O} T. Ono : On some arithmetic properties of linear algebraic groups. Annals of Math. 70 (1959) p. 266-290. | MR | Zbl | DOI

{Pe} P. Perrin : Representation de Schrödinger, indice de Maslov et groupe métaplectique. Lecture Notes in Math. 880 (1981) p. 370-407. | MR | Zbl

{Po} L. Pontrijagin : Topological groups. Princeton University press (1946). | JFM | MR

{Pu1} L. Pukanszky : Characters of algebraic solvable Lie groups. Journal of functional analysis 3 (1969) p. 435-494. | MR | Zbl | DOI

{Pu2} L. Pukanszky : Unitary representations of solvable Lie groups. Annales scientifiques de l'E.N.S. 4 (1971) p. 457-608. | MR | Zbl | EuDML | Numdam

{Pu3} L. Pukanszky : On the theory of exponential Lie groups. Transactions of the Amer. Math. Soc. 126 (1967) p. 487-507. | MR | Zbl | DOI

{Pu4} L. Pukanszky : Leçons sur les représentations de groupes. Dunod Paris (1966). | Zbl | MR

{Ri} L. Richardson : Decompositions of the $L^{2}$ -spaces of a general compact nilmanifold. Amer. Journal of Math. 93 (1971) p. 173-189. | MR | Zbl | DOI

{Ro1} J. Rosenberg : Square integrable factor representations of locally compact groups. Transactions of the Amer. Math. Soc. 237 (1978) p. 1-33. | MR | Zbl | DOI

{Ro2} J. Rosenberg : Realisations of square-integrable representations of unimodular Lie groups on $L^{2}$ cohomology spaces. Transactions of the Amer. Math. Soc. 261 (1980) p. 1-32 | MR | Zbl

{Sa} P. Samuel : Théorie algébrique des nombres. Hermann Paris (1967). | MR | Zbl

{Se} J. P. Serre : Cours d'arithmétique. Presse unversitaire de France (1970) | MR | Zbl

{Wal} N. Wallach : Harmonic analysis on homogeneous spaces. Marcel Dekker, Inc. New York (1973). | MR | Zbl

{War} G. Warner : Harmonic analysis on semi-simple Lie groups. Vol. I & II. Springer Verlag (1972). | MR | Zbl

{War} G. Warner : Harmonic analysis on semi-simple Lie groups. Vol. I | Zbl

G. Warner : Harmonic analysis on semi-simple Lie groups & II. Springer Verlag (1972). | MR | Zbl

{We1} A. Weil : L'intégration dans les groupes topologiques et ses applications. Paris (1951) | MR | Zbl | JFM

{We2} A. Weil : Sur certains groupes d'opérateurs unitaires. Acta Mathematica 111 (1964) p. 143-211. | MR | Zbl | DOI

{We3} A. Weil : Basic number theory. Springer Verlag (1969). | MR | Zbl

{We4} A. Weil : Adeles and algebraic groups. Institute for advanced study Princeton N.J. (1961).

{Wei} E. Weiss : Algebraic number theory. Mc Graw-Hill Book company, Inc. (1963) | MR