Metaplectic correspondence

Yuval Z. Flicker; David A. Kazhdan

Publications Mathématiques de l'IHÉS (1986)

  • Volume: 64, page 53-110
  • ISSN: 0073-8301

How to cite


Flicker, Yuval Z., and Kazhdan, David A.. "Metaplectic correspondence." Publications Mathématiques de l'IHÉS 64 (1986): 53-110. <>.

author = {Flicker, Yuval Z., Kazhdan, David A.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {metaplectic covering; local field; global field; Selberg trace formula; generalized Shimura correspondence; regular function; Iwahori algebra; principal series representations},
language = {eng},
pages = {53-110},
publisher = {Institut des Hautes Études Scientifiques},
title = {Metaplectic correspondence},
url = {},
volume = {64},
year = {1986},

AU - Flicker, Yuval Z.
AU - Kazhdan, David A.
TI - Metaplectic correspondence
JO - Publications Mathématiques de l'IHÉS
PY - 1986
PB - Institut des Hautes Études Scientifiques
VL - 64
SP - 53
EP - 110
LA - eng
KW - metaplectic covering; local field; global field; Selberg trace formula; generalized Shimura correspondence; regular function; Iwahori algebra; principal series representations
UR -
ER -


  1. [B] J. BERNSTEIN, P-invariant distributions, Springer Lecture Notes, 1041 (1984), 50-102. Zbl0541.22009MR86b:22028
  2. [BD] J. BERNSTEIN, rédigé par P. DELIGNE, Le «centre» de Bernstein, in [BDKV]. 
  3. [BDK] J. BERNSTEIN, P. DELIGNE, D. KAZHDAN, Trace Paley-Wiener theorem for reductive p-adic groups, J. d'Anal. Math., 1986, to appear. Zbl0634.22011MR88g:22016
  4. [BDKV] J. BERNSTEIN, P. DELIGNE, D. KAZHDAN, M.-F. VIGNERAS, Représentations des groupes réductifs sur un corps local, Paris, Hermann, 1984. Zbl0544.00007
  5. [BZ] I. N. BERNSTEIN, A. V. ZELEVINSKY, Induced representations of reductive p-adic groups I, Ann. Sci. ENS, 10 (1977), 441-472. Zbl0412.22015MR58 #28310
  6. [Bo] A. BOREL, Admissible representations with vectors fixed under an Iwahori subgroup, Invent. Math., 35 (1976), 233-259. Zbl0334.22012MR56 #3196
  7. [BJ] A. BOREL, H. JACQUET, Automorphic forms and automorphic representations, Proc. Symp. Pure Math., 33 (1979), I, 189-208. Zbl0414.22020MR81m:10055
  8. [BW] A. BOREL, N. WALLACH, Continuous cohomology, discrete subgroups, and representations of reductive groups, Ann. of Math. Studies, 94 (1980). Zbl0443.22010MR83c:22018
  9. [BN] N. BOURBAKI, Groupes et algèbres de Lie, chap. IV, V, VI, Paris, Hermann, 1968. 
  10. [C] W. CASSELMAN, Characters and Jacquet modules, Math. Ann., 230 (1977), 101-105. Zbl0337.22019MR58 #11237
  11. [C'] W. CASSELMAN, Introduction to the theory of admissible representations of p-adic reductive groups, unpublished. 
  12. [CD] L. CLOZEL, P. DELORME, Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs, Invent. Math., 77 (1984), 427-453. Zbl0584.22005MR86b:22015
  13. [DKV] P. DELIGNE, D. A. KAZHDAN, M.-F. VIGNERAS, Représentations des algèbres centrales simples p-adiques, in [BDKV]. Zbl0583.22009
  14. [D] G. VAN DIJK, Computations of certain induced characters of p-adic groups, Math. Ann., 199 (1972), 229-240. Zbl0231.22018MR49 #3043
  15. [F] Y. Z. FLICKER, Automorphic forms on covering groups of GL(2), Invent. Math., 57 (1980), 119-182. Zbl0431.10014MR81m:10057
  16. [F'] Y. Z. FLICKER, The trace formula and base change for GL(3), Springer Lecture Notes, 927 (1982), see also : Stable and labile base change for U(2), Duke Math. J., 42 (1982), 691-729. Zbl0481.10023MR84d:10035
  17. [F''] Y. Z. FLICKER, (I) Rigidity for automorphic forms, (2) Representations of simple algebras, mimeographed notes, based on a course at Harvard University, fall 1985. Zbl0656.10024
  18. ['F] Y. Z. FLICKER, On twisted lifting, Trans. AMS, 290 (1985), 161-178. Zbl0535.10031MR86j:11056
  19. [''F] Y. Z. FLICKER, On the Symmetric Square, preprint, Harvard, 1986. 
  20. [GK] I. N. GELFAND, D. A. KAZHDAN, Representations of the group GL(n, K) where K is a local field, in Lie groups and their representations, Budapest, Halsted Press, 1975, 95-118. Zbl0348.22011MR53 #8334
  21. [H] HARISH-CHANDRA, Admissible invariant distributions on reductive p-adic groups, Queen's Papers in Pure and Applied Math., 48 (1978), 281-346. Zbl0433.22012MR58 #28313
  22. [H'] HARISH-CHANDRA, Harmonic analysis on reductive p-adic groups, Proc. Symp. Pure Math., XXVI (1973), 167-192. Zbl0289.22018MR49 #5238
  23. [HD] HARISH-CHANDRA, notes by G. VAN DIJK, Harmonic analysis on reductive p-adic groups, Springer Lecture Notes, 162 (1970). Zbl0202.41101MR54 #2889
  24. [Ho] R. HOWE, The Fourier transform and germs of characters (case of GLn over a p-adic field), Math. Ann., 208 (1974), 305-322. Zbl0266.43007MR49 #7391
  25. [IM] N. IWAHORI, H. MATSUMOTO, On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. IHES, 25 (1965), 5-48. Zbl0228.20015MR32 #2486
  26. [J] H. JACQUET, On the residual spectrum of GL(n), Springer Lecture Notes, 1041 (1984), 185-208. Zbl0539.22016MR85k:22045
  27. [JS] H. JACQUET, J. SHALIKA, On Euler products and the classification of automorphic forms II, Amer. J. Math., 103 (1981), 777-815. Zbl0491.10020MR82m:10050b
  28. [K] D. KAZHDAN, On lifting, Springer Lecture Notes, 1041 (1984), 209-249. Zbl0538.20014MR86h:22029
  29. [K'] D. KAZHDAN, Cuspidal geometry on p-adic groups, J. d'Anal. Math., 1986, to appear. Zbl0634.22009MR88g:22017
  30. [KP] D. A. KAZHDAN, S. J. PATTERSON, Metaplectic forms, Publ. Math. IHES, 59 (1984), 35-142. Zbl0559.10026MR85g:22033
  31. [KP'] D. A. KAZHDAN, S. J. PATTERSON, Towards a generalized Shimura correspondance, Advances in Math., 60 (1986), 161-234. Zbl0616.10023MR87m:22050
  32. [L] G. LUSZTIG, Some examples of square-integrable representations of semi-simple p-adic groups, Trans. AMS, 277 (1983), 623-653. Zbl0526.22015MR84j:22023
  33. [Mi] J. MILNOR, An introduction to algebraic K-theory, Ann. of Math. Studies, 72 (1971). Zbl0237.18005MR50 #2304
  34. [Mo] C. MOORE, Group extensions of p-adic and adelic linear groups, Publ. Math. IHES, 35 (1968), 157-222. Zbl0159.03203MR39 #5575
  35. [R] R. R. RAO, Orbital integrals in reductive groups, Ann. of Math., 96 (1972), 505-510. Zbl0302.43002MR47 #8771
  36. [S] A. J. SILBERGER, Introduction to harmonic analysis on reductive p-adic groups, Princeton Math. Notes, 23 (1979). Zbl0458.22006MR81m:22025
  37. [S'] A. J. SILBERGER, The Knapp-Stein dimension theorem for p-adic groups, Proc. AMS, 68 (1978), 243-266 ; 69 (1979), 169-170. Zbl0348.22007MR58 #11245
  38. [St] R. STEINBERG, Lectures on Chevalley groups, Yale Lecture Notes, 1968. MR57 #6215
  39. [V] M.-F. VIGNERAS, Caractérisation des intégrales orbitales sur un groupe réductif p-adique, J. Fac. Sci. U. Tokyo, 28 (14) (1982), 945-961. Zbl0499.22011MR84b:22017
  40. [Vo] D. A. VOGAN, Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., 48 (1978), 75-98. Zbl0389.17002MR58 #22205
  41. [Z] A. V. ZELEVINSKY, Induced representations of reductive p-adic groups II, Ann. Sci. ENS, 13 (1980), 165-210. Zbl0441.22014MR83g:22012

Citations in EuDML Documents

  1. Omer Offen, Kloosterman-Fourier inversion for symmetric matrices
  2. Corinne Blondel, Uniqueness of Whittaker model for some supercuspidal representations of the metaplectic group
  3. Yuval Z. Flicker, On endo-lifting
  4. Anthony C. Kable, The tensor product of exceptional representations on the general linear group
  5. Jing-Song Huang, Metaplectic correspondences and unitary representations
  6. Yuval Z. Flicker, Distinguished representations and a Fourier summation formula
  7. Yuval Z. Flicker, Regular trace formula and base change for G L ( n )
  8. Wen-Wei Li, La formule des traces pour les revêtements de groupes réductifs connexes. IV. Distributions invariantes

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.