A Fourier summation formula for the symmetric space GL ( n ) / GL ( n - 1 )

Yuval Z. Flicker

Compositio Mathematica (1993)

  • Volume: 88, Issue: 1, page 39-117
  • ISSN: 0010-437X

How to cite


Flicker, Yuval Z.. "A Fourier summation formula for the symmetric space $\mathrm {GL}(n) / \mathrm {GL}( n-1)$." Compositio Mathematica 88.1 (1993): 39-117. <http://eudml.org/doc/90240>.

author = {Flicker, Yuval Z.},
journal = {Compositio Mathematica},
keywords = {Fourier summation formula; automorphic representations; reductive algebraic group; kernel; Selberg trace formula; reductive subgroup; Fourier decomposition; spectral decomposition},
language = {eng},
number = {1},
pages = {39-117},
publisher = {Kluwer Academic Publishers},
title = {A Fourier summation formula for the symmetric space $\mathrm \{GL\}(n) / \mathrm \{GL\}( n-1)$},
url = {http://eudml.org/doc/90240},
volume = {88},
year = {1993},

AU - Flicker, Yuval Z.
TI - A Fourier summation formula for the symmetric space $\mathrm {GL}(n) / \mathrm {GL}( n-1)$
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 88
IS - 1
SP - 39
EP - 117
LA - eng
KW - Fourier summation formula; automorphic representations; reductive algebraic group; kernel; Selberg trace formula; reductive subgroup; Fourier decomposition; spectral decomposition
UR - http://eudml.org/doc/90240
ER -


  1. [A] J. Arthur, A trace formula for reductive groups. [A1] I. Terms associated to classes in G(Q), Duke Math. J.45 (1978), 911-952; [A2] II. Applications of a truncation operator, Compos. Math.40 (1980), 87-121. Zbl0499.10033MR518111
  2. [B] J. Bernstein, An operator Paley-Wiener theorem, in preparation. 
  3. [BD] J. Bernstein, P. Deligne, Le centre de Bernstein, dans Représentation des groupes réductifs sur un corps local, Hermann, Paris (1984). Zbl0599.22016MR771671
  4. [BZ] J. Bernstein, A. Zelevinskii, [BZ1] Representations of the group GL(n, F) where F is a nonarchimedean local field, Uspekhi Mat. Nauk31 (1976), 5-70; [BZ2] Induced representations of reductive p-adic groups. I, Ann. Sci. ENS10 (1977), 441-472. Zbl0412.22015MR425030
  5. [Bi] F. Bien, D-modules and spherical representations, Princeton Univ. Press39 (1990). Zbl0723.22014MR1082342
  6. [DP] G. van Dijk, M. Poel, The irreducible unitary GL(n — 1, R)-spherical representations of SL(n, R), Compos. Math.73 (1990), 1-30. Zbl0723.22018
  7. [FJ] M. Flensted-Jensen, Discrete series for semi-simple symmetric spaces, Annals of Math.111 (1980), 253-311. Zbl0462.22006MR569073
  8. [F] Y. Flicker, [F1] Twisted tensors and Euler products, Bull. Soc. Math. France116 (1988), 295-313; [F2] On distinguished representations, J. reine angew. Math. 418 (1991), 139-172; [F3] Distinguished representations and a Fourier summation formula, Bull. Soc. Math. France (1992); [F4] Cyclic automorphic forms on a unitary group, preprint. Zbl0725.11026MR984899
  9. [FK] Y. Flicker, D. Kazhdan, A simple trace formula, J. Analyse Math.50 (1988), 189-200. Zbl0666.10018MR942828
  10. [FKS] Y. Flicker, D. Kazhdan, G. Savin, Explicit realization of a metaplectic representation, J. Analyse Math.55 (1991), 17-39. Zbl0727.11021MR1094709
  11. [GK] I. Gelfand, D. Kazhdan, Representations of GL(n, K) where K is a local field, in Lie groups and their representations, John Wiley and Sons (1975), 95-118. Zbl0348.22011
  12. [G] P. Garrett, Decomposition of Eisenstein series. Rankin triple products, Ann. of Math.125 (1987), 209-235. Zbl0625.10020MR881269
  13. [GP] B. Gross, D. Prasad, On the decomposition of a representation of SO(n) when restricted to SO(n — 1), preprint. Zbl0787.22018
  14. [HK] M. Harris, S. Kudla, The central critical value of a triple product L-function, Ann. of Math.133 (1991), 605-672. Zbl0731.11031MR1109355
  15. [J] H. Jacquet, [J1] Sur un résultat de Waldspurger, Ann. Sci. ENS.19 (1986), 185-229; [J2] On the nonvanishing of some L-functions, Proc. Indian Acad. Sci.97 (1987), 117-155. Zbl0659.10031MR868299
  16. [JPS] H. Jacquet, I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg convolutions, Amer. J. Math.105 (1983), 367-464. Zbl0525.22018MR701565
  17. [JS] H. Jacquet, J. Shalika, [JS1] On Euler products and the classification of automorphic representations, Amer. J. Math.103 (1981), I: 499-558, II: 777-815; [JS2] Rankin-Selberg convolutions: Archimedean theory; in Festschrift in Honor of I. I. Piatetski-Shapiro, IMCP2 (1990), 125-207. Zbl0712.22011
  18. [L] R. Langlands, On the functional equations satisfied by Eisenstein series, SLN544 (1976). Zbl0332.10018MR579181
  19. [M] I. Macdonald, Symmetric functions and Hall polynomials, Oxford, Clarendon Press (1979). Zbl0487.20007MR553598
  20. [MW] C. Moeglin, J.-L. Waldspurger, [MW1] Le spectre résiduel de GL(n), Ann. Sci. ENS22 (1989), 605-674; [MW2] Décomposition spectrale et series d'Eisenstein. Zbl0696.10023MR1026752
  21. [Mo] L. Morris, Eisenstein series for reductive groups over global function fields, Canad. J. Math.34 (1982), I: 91-168, II: 1112-1182. Zbl0505.22017
  22. [OM] T. Oshima, T. Matsuki, A description of discrete series for semisimple symmetric spaces, Advanced Studies in Pure Math. 4 (1984), 331-390. Zbl0577.22012MR810636
  23. [PR] I. Piatetski - Shapiro, S.Rallis, Rankin triple L-functions, Compos. Math.64 (1987), 31-115. Zbl0637.10023MR911357
  24. [P] D. Prasad, [P1] Trilinear forms for representations of GL(2) and local ε-factors, Compos. Math.75 (1990), 1-46; [P2] Invariant forms for representations of GL2 over a local field, Amer. J. Math. (1993); [P3] On the decomposition of a representation of GL(3) restricted to GL(2) over a p-adic field, Duke Math. J. (1993). 
  25. [Sh] F. Shahidi, [Sh1] On certain L-functions, Amer. J. Math.103 (1981), 297-355; [Sh2] Local coefficients and normalization of intertwining operators for GL(n), Compos. Math.48 (1983), 271-295. Zbl0506.22020MR610479
  26. [Sh] T. Shintani, On an explicit formula for class 1 "Whittaker functions" on GLn over p-adic fields, Proc. Japan Acad., 52 (1976), 180-182. Zbl0387.43002MR407208
  27. [T] M. Tadic, Classification of unitary representations in irreducible representations of general linear group, Ann. Sci. ENS19 (1986), 335-382. Zbl0614.22005MR870688
  28. [Th] E. Thoma, Die Einschränkung der Charaktere von GL(n, q) auf GL(n - 1, q), Math. Z.119(1971), 321-338. Zbl0202.02601MR288190
  29. [W] J.-L. Waldspurger, [W1] Correspondence de Shimura, J. Math. Pure Appl.59 (1980), 1-113; [W2] Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pure Appl.60 (1981), 375-484; [W3] Sur les valeurs de certaines fonctions L automorphes en leur centre de symetrie, Compos. Math.54 (1985), 173-242. Zbl0567.10021MR646366
  30. [Z] A. Zelevinsky, Induced representations of reductive p-adic groups II. On irreducible representations of GL(n), Ann. Sci. ENS13 (1980), 165-210; [Z2] Representations of finite classical groups, SLN869 (1981). Zbl0441.22014MR584084
  31. [Zh] D.P. Zhelobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, 1973. Zbl0272.22006MR473098

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.