Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II

Laurent Clozel; Patrick Delorme

Annales scientifiques de l'École Normale Supérieure (1990)

  • Volume: 23, Issue: 2, page 193-228
  • ISSN: 0012-9593

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Clozel, Laurent, and Delorme, Patrick. "Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II." Annales scientifiques de l'École Normale Supérieure 23.2 (1990): 193-228. <http://eudml.org/doc/82271>.

@article{Clozel1990,
author = {Clozel, Laurent, Delorme, Patrick},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {reductive Lie group; set of real points; reductive connected algebraic group; maximal compact subgroup; cuspidal parabolic subgroup; discrete series representations; right action; traces; basic representations; surjectivity of Harish-Chandra homomorphisms; limits of discrete series},
language = {fre},
number = {2},
pages = {193-228},
publisher = {Elsevier},
title = {Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II},
url = {http://eudml.org/doc/82271},
volume = {23},
year = {1990},
}

TY - JOUR
AU - Clozel, Laurent
AU - Delorme, Patrick
TI - Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1990
PB - Elsevier
VL - 23
IS - 2
SP - 193
EP - 228
LA - fre
KW - reductive Lie group; set of real points; reductive connected algebraic group; maximal compact subgroup; cuspidal parabolic subgroup; discrete series representations; right action; traces; basic representations; surjectivity of Harish-Chandra homomorphisms; limits of discrete series
UR - http://eudml.org/doc/82271
ER -

References

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  1. [1] J. ARTHUR, The Trace Formula in Invariant Form (Ann. Math., vol. 114, 1981, p. 1-74). Zbl0495.22006MR84a:10031
  2. [2] M. ATIYAH et W. SCHMID, A Geometric Construction of the Discrete Series for Semi-simple Lie Groups (Inv. Math., 42, 1977, p. 1-62). Zbl0373.22001MR57 #3310
  3. [3] D. BARBASCH et H. MOSCOVICI, L2-Index and the Selberg trace Formula (J. Funct. Anal., vol. 53, (2), 1983, p. 151-201). Zbl0537.58039MR85j:58137
  4. [4] J. BERNSTEIN, P. DELIGNE et D. KAZHDAN, Trace Paley-Wiener Theorem for Reductive p-adic groups (J. Anal. Math., vol. 47, 1986, p. 180-192). Zbl0634.22011MR88g:22016
  5. [5] A. BOREL et N. WALLACH, Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups, Princeton Univ. Press, 1980. Zbl0443.22010MR83c:22018
  6. [6] L. CLOZEL, On Limit Multiplicities of Discrete Series Representations in Spaces of Automorphic Forms (Inv. Math., vol. 83, 1986, p. 265-284). Zbl0582.22012MR87g:22012
  7. [7] L. CLOZEL et P. DELORME, Le Théorème de Paley-Wiener invariant pour les groupes de Lie réductifs (Inv. Math., vol. 77, 1984, p. 427-453). Zbl0584.22005MR86b:22015
  8. [8] M. COWLING, On the Paley-Wiener theorem (Inv. Math., vol. 83, 1986, p. 403-404). Zbl0591.43007MR87i:22025
  9. [9] P. DELORME, Homomorphismes de Harish-Chandra liés aux K-types minimaux des séries principales généralisées des groupes réductifs réels connexes (Ann. Sci. Ec. Norm. Sup., vol. 17, 1984, p. 117-156). Zbl0582.22009MR86b:22023
  10. [10] J. DIXMIER, Algèbres enveloppantes, Cahiers scientifiques, t. XXXVII, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR58 #16803a
  11. [11] L. EHRENPREIS, Fourier Analysis in Several Complex Variables, Wiley-Interscience Publishers, 1970. Zbl0195.10401MR44 #3066
  12. [12] S. HELGASON, Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces (Am. J. Math., vol. 86, 1964, p. 565-601). Zbl0178.17001MR29 #2323
  13. [13] S. HELGASON, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, 1978. Zbl0451.53038MR80k:53081
  14. [14] J. E. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Springer, 1972. Zbl0254.17004MR48 #2197
  15. [15] A. KNAPP, Commutativity of Intertwining Operators for Semi-simple Groups, (Compositio Math., vol. 46, 1982, p. 33-84). Zbl0488.22027MR83i:22022
  16. [16] A. KNAPP et E. STEIN, Intertwining Operators for Semi-simple Groups II (Inv. Math., vol. 60, 1980, p. 9-84). Zbl0454.22010MR82a:22018
  17. [17] A. KNAPP et G. ZUCKERMAN, Classification of Irreducible Tempred Representations of Semi-simple Groups (Ann. Math., vol. 116, 1982, p. 389-501). Zbl0516.22011MR84h:22034a
  18. [18] R. P. LANGLANDS, On the Functional Equations Satisfied by Eisenstein Series (Springer Lect. Notes, vol. 544, 1976). Zbl0332.10018MR58 #28319
  19. [19] R. P. LANGLANDS, On the Classification of Irreducible Representations of Real Algebraic Groups [Notes, I.A.S. (Princeton), 1973]. Zbl0741.22009
  20. [20] R. PARTHASARATHY, Dirac Operators and the Discrete Series (Ann. Math., vol. 93, 1972, p. 1-42). Zbl0249.22003MR47 #6945
  21. [21] M. RAÏS, Groupes linéaires compacts et fonctions C∞ covariantes (Bull. Sci. Math., vol. 107, 1983, p. 93-111). Zbl0518.22010MR85d:22028
  22. [22] P. C. TROMBI, The tempered spectrum of a real semi-simple Lie group (Am. J. Math., vol. 99, 1977, p. 57-75). Zbl0373.22007MR56 #12182
  23. [23] P. C. TROMBI, Invariant harmonic analysis on split rank one groups with applications (Pac. J. Math., vol. 101, 1982, p. 223-246). Zbl0572.22005MR84k:22015
  24. [24] D. VOGAN, The Algebraic Structure of the Representations of Semi-simple Lie Groups I (Ann. Math., vol. 109, 1979, p. 1-60). Zbl0424.22010MR81j:22020
  25. [25] D. VOGAN, The Algebraic Structure of the Representations of Semi-simple Lie Groups II, notes non publiées. 
  26. [26] D. VOGAN, Representations of Real Reductive Lie Groups, Birkhaüser, 1981. Zbl0469.22012MR83c:22022
  27. [27] D. VOGAN et G. ZUCKERMAN, Unitary Representations with Non-zero Cohomology (Compositio Math., vol. 53, 1984, p. 51-90). Zbl0692.22008MR86k:22040
  28. [28] L. CLOZEL et P. DELORME, Sur le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs réels (C. R. Acad. Sci. Paris, t. 300, série I, n° 11, 1985, p. 331-333). Zbl0593.22009MR86e:22014
  29. [29] L. CLOZEL et P. DELORME, Pseudo-coefficients et cohomologie des groupes réductifs réels (C. R. Acad. Sci. Paris, t. 300, série I, n° 12, 1985, p. 385-387). Zbl0593.22010MR87e:22032
  30. [30] HARISH-CHANDRA, Harmonic Analysis on real reductive group III (Ann. Math., vol. 104, 1976, p. 117-201). Zbl0331.22007MR55 #12875
  31. [31] A. KNAPP et G. ZUCKERMAN, Normalizing Factors, Tempered Representations, and L-groups (Proc. Symp. Pure Math., vol. 33, n° I, 1979, p. 93-105). Zbl0414.22017MR80m:22021
  32. [32] R. P. LANGLANDS, Notes on the Knapp-Zuckerman theory, Institute for Advanced Study, Princeton, 1976. 
  33. [33] D. SHELSTAD, L-Indistinguishability for Real Groups (Math. Ann., vol. 259, 1982, p. 385-430). Zbl0506.22014MR84c:22017
  34. [34] D. SHELSTAD, Orbital integrals, Endoscopic groups and L-Indistinguishability for Real Groups, in Journées Automorphes, Publ. Math., Univ. Paris-VII, Paris, p. 135-219 (s.d.). Zbl0529.22007MR85i:22019

Citations in EuDML Documents

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  1. P. Delorme, Théorème de Paley-Wiener invariant tordu pour le changement de base /
  2. Patrick Delorme, Inversion des intégrales orbitales sur certains espaces symétriques réductifs
  3. Abderrazak Bouaziz, Intégrales orbitales sur les groupes de Lie réductifs
  4. Wen-Wei Li, La formule des traces pour les revêtements de groupes réductifs connexes. IV. Distributions invariantes
  5. A. Borel, J.-P. Labesse, J. Schwermer, On the cuspidal cohomology of S -arithmetic subgroups of reductive groups over number fields
  6. Laurent Clozel, Représentations galoisiennes associées aux représentations automorphes autoduales de G L ( n )

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