Représentations de carré intégrable des groupes semi-simples réels

Michel Duflo

Séminaire Bourbaki (1977-1978)

  • Volume: 20, page 22-40
  • ISSN: 0303-1179

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Duflo, Michel. "Représentations de carré intégrable des groupes semi-simples réels." Séminaire Bourbaki 20 (1977-1978): 22-40. <http://eudml.org/doc/109920>.

@article{Duflo1977-1978,
author = {Duflo, Michel},
journal = {Séminaire Bourbaki},
keywords = {discrete series representations; semisimple Lie groups; Harish-Chandra's parametrization; Blattner conjecture},
language = {fre},
pages = {22-40},
publisher = {Springer-Verlag},
title = {Représentations de carré intégrable des groupes semi-simples réels},
url = {http://eudml.org/doc/109920},
volume = {20},
year = {1977-1978},
}

TY - JOUR
AU - Duflo, Michel
TI - Représentations de carré intégrable des groupes semi-simples réels
JO - Séminaire Bourbaki
PY - 1977-1978
PB - Springer-Verlag
VL - 20
SP - 22
EP - 40
LA - fre
KW - discrete series representations; semisimple Lie groups; Harish-Chandra's parametrization; Blattner conjecture
UR - http://eudml.org/doc/109920
ER -

References

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  1. [1] A. Andreotti et E. Vesentini - Carleman estimates for the Laplace-Beltrami equations on complex manifolds, I.H.E.S. Pub. Math., 25 (1965), 313-362. Zbl0138.06604MR175148
  2. [2] M.F. Atiyah - Elliptic operators, discrete groups and von Neumann algebras, Astérisque32/33 (1976), 43-72. Zbl0323.58015MR420729
  3. [3] M.F. Atiyah et W. Schmid - A new proof of the regularity theorem for invariant eigendistributions on semisimple Lie groups, à paraître 
  4. [4] M.F. Atiyah et W. Schmid - A geometric construction of the discrete series for semisimple Lie groups, Inv. Math., 42 (1977), 1-62. Zbl0373.22001MR463358
  5. [5] V. Bargmann - Irreducible unitary representations of the Lorentz group, Ann. of Math., 48 (1947), 568-640. Zbl0045.38801MR21942
  6. [6] A. Borel - Compact Clifford-Klein forms of symmetric spaces, Topology, 2 (1963), 111-122. Zbl0116.38603MR146301
  7. [7] A. Borel et N. Wallach - Seminar notes on the cohomology of discret subgroups of semi-simple groups, à paraître. 
  8. [8] J. Carmona - Fibrés vectoriels holomorphes sur une variété hermitienne, Math. Ann., 205 (1973), 89-112. Zbl0238.22013
  9. [9] J. Dixmier - Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris1964. Zbl0152.32902MR171173
  10. [10] J. Dixmier - Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR498737
  11. [11] T.J. Enright - Blattner type multiplicity formulas for the fundamental series of a real semisimple Lie algebra, Ann. Sc. Ec. Norm. Sup., XI(1978),fasc.4. 
  12. [12] T.J. Enright et V.S. Varadarajan - On a infinitésimal characterization of the discrete series, Ann. of Math., 102 (1975), 1-15. Zbl0304.22011MR476921
  13. [13] Harish- Chandra - Discrete series for semi-simple Lie groups I, II, Acta Math., 113 (1965), 241-318 ; 116 (1966), 1-111. Zbl0199.20102
  14. [14] Harish- Chandra - Harmonic analysis on semi-simple Lie groups, Bull. Amer. Math. Soc., 76 (1970), 529-551. Zbl0212.15101MR257282
  15. [15] H. Hecht et W. Schmid - A proof of Blattner's conjecture, Inventiones Math., 31 (1975), 129-154. Zbl0319.22012MR396855
  16. [16] H. Hecht et W. Schmid - On integrable representations of a semi-simple Lie group, Math. Annalen, 220(1976), 147-150. Zbl0363.22008MR399358
  17. [17] T. Hiraï - The characters of the discrete series for semisimple Lie groups, à paraître. Zbl0484.22019
  18. [18] R. Hotta - On realization of discrete series for semisimple Lie groups, Proc. Japan Acad., 46 (1970), 993-996. Zbl0229.22028MR291354
  19. [19] R. Hotta et R. Parthasarathy - Multiplicity formulae for discrete series, Inventiones Math., 26 (1974), 133-178. Zbl0298.22013MR348041
  20. [20] N.E. Hurt - Proof of an analogue of a conjecture of Langlands for the "Heisenberg-Weyl" group, Bull. London Math. Soc., 4 (1972), 127-129. Zbl0268.22008MR330354
  21. [21] A.A. Kirillov - Unitary representation of nilpotent Lie groups, Russ. Math. Surveys, 17 (1962), 53-104. Zbl0106.25001MR142001
  22. [22] A.W. Knapp et N. Wallach - Szëgo kernels associated with discrete series, Inventiones Math., (1976), 163-200. Zbl0332.22015MR419686
  23. [23] B. Kostant - Orbits, symplectic structures, and représentation theory, Proc. U.S.-Japan Seminar Diff. Geometry, Kyoto, Japan 1965. Zbl0141.02701MR213476
  24. [24] R.P. Langlands - Dimension of spaces of automorphic forms, Proc. Symposia in Pure Math., IX (1966), 253-257. Zbl0215.11802MR212135
  25. [25] R.P. Langlands - On the classification of irreducible representations of real algebraic groups, à paraître. Zbl0741.22009
  26. [26] D. Miličič - Asymptotic behaviour of matrix coefficients of the discret series, Duke Math. Journal, 44 (1977), 59-88. Zbl0398.22022MR430164
  27. [27] M.S. Narasimhan et K. Okamoto - An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of non compact type, Ann. of Math., 91 (1970), 486-511. Zbl0257.22013MR274657
  28. [28] R. Parthasarathy - Dirac operator and the discrete series, Ann. of Math., 96 (1972), 1-30. Zbl0249.22003MR318398
  29. [29] I. Satake - Unitary representations of a semi-direct product of Lie groups on ∂-cohomology spaces, Math. Annalen, 190 (1971), 177-202. Zbl0205.04405
  30. [30] W. Schmid - Homogeneous complex manifolds and representations of semisimple Lie groups, Thesis, Berkeley, 1967. MR225930
  31. [31] W. Schmid - On a conjecture of Langlands, Ann. of Math., 93(1971), 1-42 Zbl0291.43013MR286942
  32. [32] W. Schmid - On the characters of discrete series (the hermitian-symmetric case)Inventiones Math., 30 (1975), 47-144. Zbl0324.22007MR396854
  33. [33] W. Schmid - Some properties of square integrable representations of semisimple Lie groups, Ann. of Math., 102 (1975), 535-564. Zbl0347.22011MR579165
  34. [34] W. Schmid - Two character identities for semisimple Lie groups, Lecture Notes in Math., n° 587, 1977, Springer, 196-225. Zbl0362.22015MR507247
  35. [35] W. Schmid - L2-cohomology and the discrete series, Ann. of Math., 103 (1976), 375-394. Zbl0333.22009MR396856
  36. [36] M.W. Silva - The Embeddings of the discrete series in the principal series for semisimple Lie group of real rank one, Thesis, Rutgers Univ., 1977. 
  37. [37] P.C. Trombi et V.S. Varadarajan - Asymptotic behaviour of eigenfunctions on a semisimple Lie group ; The discrète spectrum, Acta Math., 129 (1972), 237- 280. Zbl0244.43006MR393349
  38. [38] V.S. Varadarajan - The theory of characters and the discrete series for semi-simple Lie groups, Proc. Symposia in Pure Math., 26 (1973), 45-99. Zbl0295.22014MR409730
  39. [39] V.S. Varadarajan - Harmonic analysis on real reductive groups, Lecture Notes in Math., n° 576, 1977, 1-521. Zbl0354.43001MR473111
  40. [40] J.A. Vargas - A character formula for the discrete series of a semisimple Lie group, Thesis, Columbia Univ., 1977. 
  41. [41] D. Vogan - Lie algebra cohomology and the representations of semisimple Lie groups,Thesis, M.I.T., 1976. 
  42. [42] N. Wallach - On the Enright-Varadarajan modules : a construction of the discrete series, Ann. Sc. Ec. Norm. Sup., 9 (1976), 81-102. Zbl0379.22008MR422518
  43. [43] G. Warner - Harmonic analysis on semisimple Lie groups, I et II, Springer Verlag, Berlin, 1972. Zbl0265.22020
  44. [44] J.A. Wolf - Essential self-adjointness for the Dirac operator and its square, Indiana Univ. Math., 22 (1973), 611-640. Zbl0263.58013MR311248
  45. [45] G. Zuckerman - Tensor product of finite and infinite dimensional representations of semisimple Lie groups, à paraître dans Annals of Math. Zbl0384.22004
  46. D.L. Degeorge et N.R. Wallach - Limit formulas for multiplicities in L2(Γ). Zbl0397.22007
  47. M. Flensted-Jensen - On a fundamental series of representations related to an affine symmetric space. Zbl0421.22007

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