Representations of semisimple groups associated to nilpotent orbits

Linda Preiss Rothschild; Joseph A. Wolf

Annales scientifiques de l'École Normale Supérieure (1974)

  • Volume: 7, Issue: 2, page 155-173
  • ISSN: 0012-9593

How to cite

top

Rothschild, Linda Preiss, and Wolf, Joseph A.. "Representations of semisimple groups associated to nilpotent orbits." Annales scientifiques de l'École Normale Supérieure 7.2 (1974): 155-173. <http://eudml.org/doc/81933>.

@article{Rothschild1974,
author = {Rothschild, Linda Preiss, Wolf, Joseph A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {2},
pages = {155-173},
publisher = {Elsevier},
title = {Representations of semisimple groups associated to nilpotent orbits},
url = {http://eudml.org/doc/81933},
volume = {7},
year = {1974},
}

TY - JOUR
AU - Rothschild, Linda Preiss
AU - Wolf, Joseph A.
TI - Representations of semisimple groups associated to nilpotent orbits
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1974
PB - Elsevier
VL - 7
IS - 2
SP - 155
EP - 173
LA - eng
UR - http://eudml.org/doc/81933
ER -

References

top
  1. [1] L. AUSLANDER and B. KOSTANT, Polarization and Unitary Representations of Solvable Lie Groups (Inventiones Math., 14, 1971, p. 255-354). Zbl0233.22005MR45 #2092
  2. [2] R. J. BLATTNER, On induced representations, II : Infinitesimal induction (Amer. J. Math., vol. 83, 1961, p. 499-512). Zbl0139.07702MR26 #2885
  3. [3] É. CARTAN, La géométrie des groupes simples (Annali di Mat., vol. 4, 1927, p. 209-256). Zbl53.0392.03JFM53.0392.03
  4. [4] N. CONZE and M. DUFLO, Sur l'algèbre enveloppante d'une algèbre de Lie résoluble (Bull. Soc. Math. Fr. t. 94, 1970, p. 201-208). Zbl0202.04101MR44 #270
  5. [5] M. DUFLO, Caractères des groupes et des algèbres de Lie résolubles (Ann. scient. Éc. Norm. Sup., t. 3, 1970, p. 23-74). Zbl0223.22016MR42 #4672
  6. [6] M. DUFLO, Sur les extensions des représentations irréductibles des groupes de Lie nilpotents (Ann. scient. Éc. Norm. Sup., t. 5, 1972, p. 71-120). Zbl0241.22030MR46 #1966
  7. [7] G. B. ELKINGTON, Centralizers of unipotent elements in semisimple algebraic groups (J. Algebra, vol. 23, 1972, p. 137-163). Zbl0247.20053MR46 #7342
  8. [8] HARISH-CHANDRA, On some applications of the universal enveloping algebra of a semisimple Lie algebra (Trans. Amer. Math. Soc., vol. 70, 1951, p. 28-96). Zbl0042.12701MR13,428c
  9. [9] HARISH-CHANDRA, Harmonic analysis on semisimple Lie groups (Bull. Amer. Math. Soc., vol. 76, 1970, p. 529-551). Zbl0212.15101MR41 #1933
  10. [10] HARISH-CHANDRA, On the theory of the Eisenstein integral, Springer-Verlag (Lecture Notes in Math., vol. 266, 1971, p. 123-149). Zbl0245.22019MR53 #3200
  11. [11] A. A. KIRILLOV, Unitary representations of nilpotent Lie groups (Uspeki Mat. Nauk., 17, 1962, p. 57-110). Zbl0106.25001MR25 #5396
  12. [12] B. KOSTANT, The principal three dimensional subgroup and the Betti numbers of a complex simple Lie group (Amer. J. Math., vol. 81, 1959, p. 973-1032). Zbl0099.25603MR22 #5693
  13. [13] B. KOSTANT, Lie group representations on polynomial rings (Amer. J. Math., vol. 85, 1963, p. 327-404). Zbl0124.26802MR28 #1252
  14. [14] B. KOSTANT, Quantization and unitary representations, Springer-Verlag (Lecture Notes in Math., vol. 170, 1970, p. 87-207). Zbl0223.53028MR45 #3638
  15. [15] B. KOSTANT and S. RALLIS, Orbits and representations associated with symmetric spaces (Amer. J. Math., vol. 93, 1971, p. 753-809). Zbl0224.22013MR47 #399
  16. [16] H. MATSUMOTO, Quelques remarques sur les groupes de Lie algébriques réels (J. Math. Soc. Japan, vol. 16, 1964, p. 419-446). Zbl0133.28706MR32 #1292
  17. [17] C. C. MOORE, Representations of solvable and nilpotent groups and harmonic analysis on nil- and solvmanifolds (Amer. Math. Soc. Proceedings of Symposia in Pure Math., vol. 26, 1973, p. 3-44). Zbl0292.22015MR52 #5871
  18. [18] H. OZEKI and M. WAKIMOTO, On polarizations of certain homogeneous spaces (Hiroshima Math. J., vol. 2, 1972, p. 445-482). Zbl0267.22011MR49 #5236a
  19. [19] L. PUKÁNSZKY, On the unitary representations of exponential groups (J. Functional Analysis, vol. 2, 1968, p. 73-113). Zbl0172.18502MR37 #4205
  20. [20] L. PUKÁNSKYCharacters of algebraic solvable groups (J. Functional Analysis, vol. 3, 1969, p. 435-494). Zbl0186.20004MR40 #1539
  21. [21] S. RALLIS, Lie group representations associated to symmetric spaces, thesis, M. I. T., 1968. 
  22. [22] M. WAKIMOTO, Polarizations of certain homogeneous spaces and most continuous principal series (Hiroshima Math. J., vol. 2, 1972, p. 483-533). Zbl0267.22012MR49 #5236b
  23. [23] G. WARNER, Harmonic Analysis on Semisimple Lie Groups I, II (Grundlehren Math. Wissensch., vol. 188, and 189, Springer-Verlag, 1972). Zbl0265.22020
  24. [24] J. A. WOLF, The action of a real semisimple group a on complex flag manifold, I : Orbit structure and holomorphic arc components (Bull. Amer. Math. Soc., vol. 75, 1969, p. 1121-1237). Zbl0183.50901MR40 #4477
  25. [25] J. A. WOLF, The action of a real semisimple group on a complex flag manifold, II : Unitary representations on partially holomorphic cohomology spaces [Memoirs Amer. Math. Soc., Number 138, 1974]. Zbl0288.22022MR52 #14160
  26. [26] J. A. WOLF, Partially harmonic spinors and representations of reductive Lie groups [J. Funct. Anal., vol. 15, 1974, p. 117-154]. Zbl0279.22009MR52 #14161
  27. [27] P. BERNAT, N. CONZE, M. DUFLO, M. LÉVY-NAHAS, M. RAIS, P. RENOUARD et M. VERGNE, Représentations des Groupes de Lie Résolubles, Dunod, Paris, 1972. Zbl0248.22012MR56 #3183

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.