Projection d'orbites, formule de Kirillov et formule de Blattner

Michel Duflo; Gerrit Heckman; Michele Vergne

Mémoires de la Société Mathématique de France (1984)

  • Volume: 15, page 65-128
  • ISSN: 0249-633X

How to cite

top

Duflo, Michel, Heckman, Gerrit, and Vergne, Michele. "Projection d'orbites, formule de Kirillov et formule de Blattner." Mémoires de la Société Mathématique de France 15 (1984): 65-128. <http://eudml.org/doc/94846>.

@article{Duflo1984,
author = {Duflo, Michel, Heckman, Gerrit, Vergne, Michele},
journal = {Mémoires de la Société Mathématique de France},
keywords = {Kirillov formula; representation of semisimple Lie groups; Blattner formula; compactly embedded Cartan algebra; Weyl group; orbit; generalized function},
language = {fre},
pages = {65-128},
publisher = {Société mathématique de France},
title = {Projection d'orbites, formule de Kirillov et formule de Blattner},
url = {http://eudml.org/doc/94846},
volume = {15},
year = {1984},
}

TY - JOUR
AU - Duflo, Michel
AU - Heckman, Gerrit
AU - Vergne, Michele
TI - Projection d'orbites, formule de Kirillov et formule de Blattner
JO - Mémoires de la Société Mathématique de France
PY - 1984
PB - Société mathématique de France
VL - 15
SP - 65
EP - 128
LA - fre
KW - Kirillov formula; representation of semisimple Lie groups; Blattner formula; compactly embedded Cartan algebra; Weyl group; orbit; generalized function
UR - http://eudml.org/doc/94846
ER -

References

top
  1. [B-V] D. BARBASCH, D.A. VOGAN : Sketch of proof of Rossmann's character formula (Non publié). 
  2. [Be-Ve.1] N. BERLINE et M. VERGNE : Fourier transform of orbits of the coadjoint representation. Representation theory of reductive groups, Birkhauser, Boston, 1983. Zbl0527.22010
  3. [Be-Ve.2] N. BERLINE et M. VERGNE : The equivariant index and Kirillov's character formula, à paraître dans American Journal of Mathematics. Zbl0604.58046
  4. [Be-Ve.3] N. BERLINE et M. VERGNE : Classes caractéristiques équivariantes, Formule de localisation en cohomologie équivariante, Comptes Rendus Acad. Sci. Paris, 295 (1982), pp. 539-541. Zbl0521.57020MR83m:58002
  5. [Bo] R. BOTT : Vector fields and characteristic numbers, Mich. Math. Journal, 14 (1967), pp. 231-244. Zbl0145.43801MR35 #2297
  6. [C-R] A. CEREZO et F. ROUVIERE : Solution élémentaire d'un opérateur invariant à gauche sur un groupe de Lie compact. Ann. Sci. Ec. Norm. Sup. 2 (1969), pp. 561-581. Zbl0191.43801MR42 #6869
  7. [D] M. DUFLO : Construction de représentations unitaires d'un groupe de Lie. In "Harmonic analysis and group representations." C.I.M.E. 1980, ed. Liguori, Naples 1982. 
  8. [Dui] J.J. DUISTERMAAT : Fourier integral operators. Courant Institute, New-York (1973). Zbl0272.47028MR56 #9600
  9. [D-H] J.J. DUISTERMAAT et G.J. HECKMAN : On the variation in the cohomology of the symplectic form of the reduced phase space. Inventiones Math. 69 (1982), pp. 259-268. Zbl0503.58015MR84h:58051a
  10. [E] T.J. ENRIGHT : On the fundamental series of a real semi-simple Lie algebra : their irreducibility, resolutions and multiplicity formulae. Annals of Math. 110 (1979), pp. 1-82. Zbl0417.17005MR81a:17003
  11. [G-St.1] V. GUILLEMIN et S. STERNBERG : Geometric asymptotics. Maths Surveys no 14, A.M.S. Rhode Island (1977). Zbl0364.53011MR58 #24404
  12. [G-St.2] V. GUILLEMIN et S. STERNBERG : Convexity properties of the moment mapping. Inventiones Math. 67 (1982), pp. 491-513. Zbl0503.58017MR83m:58037
  13. [H-C.1] HARISH-CHANDRA : The characters of semi-simple Lie groups. Trans. Amer. Math. Soc. 83 (1956), pp. 98-163. Zbl0072.01801MR18,318c
  14. [H-C.2] HARISH-CHANDRA : Invariant eigen-distributions on a semi-simple Lie group. Trans. Amer. Math. Soc. 119 (1965), pp. 457-508. Zbl0199.46402MR31 #4862d
  15. [H-C.3] HARISH-CHANDRA : Discrete series for semi-simple Lie groups I. Construction of invariant eigendistributions. Acta Mathematica, 113 (1965), pp. 242-318. Zbl0152.13402MR36 #2744
  16. [H-C.4] HARISH-CHANDRA : Discrete series for semi-simple Lie groups II Acta Mathematica, 116 (1966), pp. 1-111. Zbl0199.20102MR36 #2745
  17. [He-S.1] H. HECHT et W. SCHMID : A proof of Blattner's conjecture. Inventiones math., 31 (1975), pp. 129-154. Zbl0319.22012MR53 #715
  18. [He-S.2] H. HECHT et W. SCHMID : Characters, asymptotic and n-homology of Harish-Chandra modules. Acta Mathematica, 151 (1983), pp. 49-151. Zbl0523.22013MR84k:22026
  19. [He] G.J. HECKMAN : Projections of orbits and asymptotic behaviour of multiplicities for compact connected Lie groups. Inventiones math. 67 (1982), pp. 333-356. Zbl0497.22006MR84d:22019
  20. [Kh] M.S. KHALGUI : Caractères des groupes de Lie. Journal of functional analysis, 47 (1982), pp. 64-77. Zbl0507.22009MR84f:22020
  21. [Ki] A.A. KIRILLOV : Eléments de la théorie des représentations. Ed. M.I.R Moscou, (1974). MR52 #14134
  22. [L-Ve] G. LION et M. VERGNE : The Weil representation, Maslov index and theta series. Birkhäuser, Boston (1980). Zbl0444.22005
  23. [P] S. PANEITZ : Communication personnelle (1983). 
  24. [R] W. ROSSMANN : Kirillov's character formula for reductive Lie groups. Inventiones math., 48 (1978), pp. 207-220. Zbl0372.22011MR81g:22012
  25. [S] W. SCHMID : On the characters of discrete series (the Hermitian symmetric case). Inventiones math., 30 (1975), pp. 47-144. Zbl0324.22007MR53 #714
  26. [T] P. TORASSO : Sur le caractère de la représentation de Shale-Weil de Mp(n, ℝ) et Sp (n, ℂ). Math. Ann., 252 (1980), pp. 53-86. Zbl0452.22015MR82a:22019
  27. [Ve] M. VERGNE : On Rossmann's character formula for discrete series. Inventiones Math., 54 (1979), pp. 11-14. Zbl0428.22010MR81d:22017

Citations in EuDML Documents

top
  1. Elisa Prato, Siye Wu, Duistermaat-Heckman measures in a non-compact setting
  2. Abderrazak Bouaziz, Formule d'inversion d'intégrales orbitales tordues
  3. P. Delorme, Théorème de Paley-Wiener invariant tordu pour le changement de base /
  4. Patrick Delorme, Inversion des intégrales orbitales sur certains espaces symétriques réductifs
  5. Mohamed Salah Khalgui, Pierre Torasso, La formule du caractère pour les groupes de Lie presque algébriques réels
  6. Stéphane Guillermou, Index of transversally elliptic D-modules
  7. Paul-Émile Paradan, Spinc-quantization and the K-multiplicities of the discrete series

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.