Représentation métaplectique et conjectures de Howe

Jean-Loup Waldspurger

Séminaire Bourbaki (1986-1987)

  • Volume: 29, page 85-99
  • ISSN: 0303-1179

How to cite


Waldspurger, Jean-Loup. "Représentation métaplectique et conjectures de Howe." Séminaire Bourbaki 29 (1986-1987): 85-99. <>.

author = {Waldspurger, Jean-Loup},
journal = {Séminaire Bourbaki},
language = {fre},
pages = {85-99},
publisher = {Société Mathématique de France},
title = {Représentation métaplectique et conjectures de Howe},
url = {},
volume = {29},
year = {1986-1987},

AU - Waldspurger, Jean-Loup
TI - Représentation métaplectique et conjectures de Howe
JO - Séminaire Bourbaki
PY - 1986-1987
PB - Société Mathématique de France
VL - 29
SP - 85
EP - 99
LA - fre
UR -
ER -


  1. [1] A. Albert - Structure of algebras, Amer. Math. Soc. Coll. Publ.XXIV, Providence1961. MR123587JFM65.0094.02
  2. [2] A. Borel, H. Jacquet, Automorphic forms and automorphic representations, in Automorphic forms, representations and L-functions, p. 189-202, Proc. of Symp. in Pure Math.XXXIII, Part 1, AMS, Providence1979. Zbl0414.22020MR546598
  3. [3] F. Bruhat, Représentations des groupes localement compacts 2, cours à Paris7, multigraphié ENS1971. 
  4. [4] M. Eichler, Quadratische Formen und orthogonale Gruppen, Springer, BerlinHeidelbergNew-York1974. Zbl0277.10017MR351996
  5. [5] E. Hecke, Analytische Arithmetik der positiven quadratischen Formen, in Mathematische Werke, Vandenhoeck Ruprecht, Göttingen1970. Zbl0024.00902MR104550
  6. [6] R. Howe, θ-series and invariant theory, in Automorphic forms, representations and L-functions, p.275-286, Proc. of Symp. in Pure Math.XXXIII, Part 1, AMS, Providence1979. Zbl0423.22016
  7. [7] R. Howe, Transcending classical invariant theory, preprint. Zbl0716.22006MR985172
  8. [8] R. Howe, Invariant theory and duality for classical groups over finite fields, with applications to their singular representation theory, preprint. 
  9. [9] M. Kashiwara, M. Vergne, On the Segal-Shale-Weil representations and harmonic polynomials, Inv. Math.44 (1978), 1-47. Zbl0375.22009MR463359
  10. [10] M. Kneser, Approximation in algebraischen Gruppen, Colloque sur la théorie des groupes algébriques, Bruxelles1962. 
  11. [11] S. Kudla, On the local theta correspondence, Inv. Math.83 (1986), 229-255. Zbl0583.22010MR818351
  12. [12] G. Lion, M. Vergne, The Weil representation, Maslov index and theta series, Progress in Math.6, Birkhäuser, BostonBaselStuttgart1980. Zbl0444.22005MR573448
  13. [13] G. Mackey, A theorem of Stone and Von Neumann, Duke Math. J.16 (1949) 313-326. Zbl0036.07703MR30532
  14. [14] J. Von Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren, Math. Ann.104 (1931), 570-578. Zbl0001.24703MR1512685
  15. [15] P. Perrin, Représentations de Schrödinger, indice de Maslov et groupe métaplectique, in Non commutative harmonic analysis and Lie groups, Proc. Marseille-Luminy1980, Springer LN880, BerlinHeidelbergNew-York. Zbl0462.22008MR644841
  16. [16] S. Rallis, On the Howe duality conjecture, Comp. Math.51 (1984), 333-399. Zbl0624.22011MR743016
  17. [17] S. Rallis, Injectivity properties of liftings associated to Weil representations, Comp. Math.52 (1984), 139-169. Zbl0624.22012MR750352
  18. [18] R. Rad, On some explicit formulas in the theory of Weil representations, preprint. 
  19. [19] C. Siegel, Gesammelte Abhandlungen I, Springer1966. Zbl0143.00101MR197270
  20. [20] M. Stone, Linear transformations in Hilbert space III, operational methods and group theory, Proc. Nat. Acad. Sci. USA16 (1930), 172-175. Zbl56.0357.01JFM56.0357.01
  21. [21] A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math.111, (1964), 143-211. Zbl0203.03305MR165033
  22. [22] A. Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math.113 (1965), 1-87. Zbl0161.02304MR223373

NotesEmbed ?


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.