Distinguished representations and a Fourier summation formula

Yuval Z. Flicker

Bulletin de la Société Mathématique de France (1992)

  • Volume: 120, Issue: 4, page 413-465
  • ISSN: 0037-9484

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Flicker, Yuval Z.. "Distinguished representations and a Fourier summation formula." Bulletin de la Société Mathématique de France 120.4 (1992): 413-465. <http://eudml.org/doc/87651>.

@article{Flicker1992,
author = {Flicker, Yuval Z.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {distinguished representation; summation formula; relative trace formula},
language = {eng},
number = {4},
pages = {413-465},
publisher = {Société mathématique de France},
title = {Distinguished representations and a Fourier summation formula},
url = {http://eudml.org/doc/87651},
volume = {120},
year = {1992},
}

TY - JOUR
AU - Flicker, Yuval Z.
TI - Distinguished representations and a Fourier summation formula
JO - Bulletin de la Société Mathématique de France
PY - 1992
PB - Société mathématique de France
VL - 120
IS - 4
SP - 413
EP - 465
LA - eng
KW - distinguished representation; summation formula; relative trace formula
UR - http://eudml.org/doc/87651
ER -

References

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  1. [A] ARTHUR (J.). — A trace formula for reductive groups, [A1], I. Terms associated to classes in G(Q), Duke Math. J., t. 45, 1978, p. 911-952, and [A2], II. Applications of a truncation operator, Compositio Math., t. 40, 1980, p. 87-121. Zbl0499.10032
  2. [BZ] BERNSTEIN (J.) and ZELEVINSKII (A.). — Representations of the group GL(n, F) where F is a nonarchimedean local field, Uspekhi Mat. Nauk, t. 31, 1976, p. 5-70, and [BZ1], Induced representations of reductive p-adic groups. I, Ann. Sci. École Norm. Sup., t. 10, 1977, p. 441-472. Zbl0412.22015
  3. [B] BIEN (F.). — D-modules and spherical representations. — Princeton Univ. Press, 39, 1990. Zbl0723.22014MR92f:22025
  4. [BH] BOPP (N.) et HARINCK (P.). — Formule de Plancherel pour GL(n, ℂ)/U(p, q), Math. Gottingensis, t. 27, 1990, p. 1-52. 
  5. [D] DELORME (P.). — Coefficients généralisés de séries principales sphériques et distributions sphériques sur G(ℂ)/G(ℝ), Invent. Math., t. 105, 1991, p. 305-346. Zbl0741.43010MR92j:22027
  6. [FJ] FLENSTED-JENSEN (M.). — Discrete series for semi-simple symmetric spaces, Ann. of Math., t. 111, 1980, p. 253-311. Zbl0462.22006MR81h:22015
  7. [F] FLICKER (Y.). — [F1], On distinguished representations, J. Reine Angew. Math., t. 418, 1991, p. 139—172 and [F2], Twisted tensors and Euler products, Bull. Soc. Math. France, t. 116, 1988, p. 295-313, and [F3], Stable and labile base change for U(2), Duke Math. J., t. 49, 1982, p. 691-729, and [F4] Packets and liftings for U(3), J. Analyse Math, t. 50, 1988, p. 19-63, and [F5], On the local twisted tensor L-function, preprint. MR92i:22019
  8. [FK] FLICKER (Y.) and KAZHDAN (D.). — [FK1], Metaplectic correspondence, Publ. Math. IHES, t. 64, 1987, p. 53-110, and [FK2], A simple trace formula, J. Analyse Math., t. 50, 1988, p. 189-200. Zbl0616.10024
  9. [GK] GELFAND (I.) and KAZHDAN (D.). — Representations of GL(n, K) where K is a local field, in Lie groups and their representations, John Wiley and Sons, 1975, p. 95-118. Zbl0348.22011MR53 #8334
  10. [JPS] JACQUET (H.), PIATETSKI-SHAPIRO (I.) and SHALIKA (J.). — Rankin-Selberg convolutions, Amer. J. Math., t. 105, 1983, p. 367-464. Zbl0525.22018MR85g:11044
  11. [JS] JACQUET (H.) and SHALIKA (J.). — On Euler products and the classification of automorphic representations, Amer. J. Math., t. 103, 1981, p. I : 499-558, II : 777-815, and [JS1] Rankin-Selberg convolutions : Archimedean theory, in Piatetski-Shapiro Festchrift I, IMCP, t. 2, 1990, p. 125-207. Zbl0473.12008MR82m:10050a
  12. [K] KEYS (D.). — [K1], Principal series representations of special unitary groups over local field, Compositio Math., t. 51, 1984, p. 115-130, and [K2] L-indistinguishability and R-groups for quasi-split groups ; unitary groups in even dimension, Ann. Sci. École Norm. Sup., t. 20, 1987, p. 31-64. Zbl0547.22009MR85d:22031
  13. [L] LANGLANDS (R.). — [L1], Problems in the theory of automorphic forms, in Modern Analysis and applications, SLN, t. 170, 1970, p. 18-86, and [L2], On the functional equations satisfied by Eisenstein series, SLN, t. 544, 1976, and [L3], Book review of The Theory of Eisenstein Systems, by S. Osborne and G. Warner, Academic Press, New-York 1981, Bull. AMS, t. 9, 1983, p. 351-361. MR46 #1758
  14. [MW] MOEGLIN (C.) et WALDSPURGER (J.-L). — [MW1], Le spectre résiduel de GL(n), Ann. Sci. École Norm. Sup., t. 22, 1989, p. 605-674, and [MW2], Décomposition spectrale et séries d'Eisenstein. Zbl0696.10023MR91b:22028
  15. [M] MORRIS (L.). — Eisenstein series for reductive groups over global function fields, Canad. J. Math., t. 34, 1982, I : p. 91-168, II : p. 1112-1182. Zbl0499.22021MR84j:22024a
  16. [OM] OSHIMA (T.) and MATSUKI (T.). — A description of discrete series for semisimple symmetric spaces, Adv. Stud. Pure Math., t. 4, 1984, p. 331-390. Zbl0577.22012MR87m:22042
  17. [S] SANO (S.). — Invariant spherical distributions and the Fourier inversion formula on GL(n, ℂ)/GL(n, ℝ), J. Math. Soc. Japan, t. 36, 1984, p. 191-219. Zbl0545.43010MR85h:43011
  18. [Sh] SHAHIDI (F.). — [Sh1], On certain L-functions, Amer. J. Math., t. 103, 1981, p. 297-355, and [Sh2], Fourier transforms of intertwining operators and Plancherel measures for GL(n), Amer. J. Math., t. 104, 1982, p. 67-111, and [Sh3], Local coefficients and normalization of intertwining operators for GL(n), Compositio Math., t. 48, 1983, p. 271-295. MR82i:10030
  19. [T] TADIC (M.). — Classification of unitary representations in irreducible representations of general linear group, Ann. Sci. École Norm. Sup., t. 19, 1986, p. 335-382. Zbl0614.22005MR88b:22021
  20. [V] VOGAN (D.). — Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., t. 48, 1978, p. 75-98. Zbl0389.17002MR58 #22205
  21. [W] WALDSPURGER (J.-L.). — Correspondence de Shimura, J. Math. Pures Appl., t. 59, 1980, p. 1-113, and Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl., t. 60, 1981, p. 375-484. Zbl0431.10015
  22. [Z] ZELEVINSKY (A.). — Induced representations of reductive p-adic groups, II. On irreducible representations of GL(n), Ann. Sci. École Norm. Sup., t. 13, 1980, p. 165-210. Zbl0441.22014MR83g:22012

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