@incollection{AST_2012__346__1_0, author = {Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra}, title = {Symplectic local root numbers, central critical $L$-values, and restriction problems in the representation theory of classical groups}, booktitle = {Sur les Conjectures de Gross et Prasad. I}, editor = {Gan, W. T. and Gross, B. H. and Prasad, D. and Waldspurger, J.-L.}, series = {Ast\'erisque}, pages = {1--109}, publisher = {Soci\'et\'e math\'ematique de France}, number = {346}, year = {2012}, mrnumber = {3202556}, zbl = {1280.22019}, language = {en}, url = {http://www.numdam.org/item/AST_2012__346__1_0/} }
TY - CHAP AU - Gan, Wee Teck AU - Gross, Benedict H. AU - Prasad, Dipendra TI - Symplectic local root numbers, central critical $L$-values, and restriction problems in the representation theory of classical groups BT - Sur les Conjectures de Gross et Prasad. I AU - Collectif ED - Gan, W. T. ED - Gross, B. H. ED - Prasad, D. ED - Waldspurger, J.-L. T3 - Astérisque PY - 2012 SP - 1 EP - 109 IS - 346 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2012__346__1_0/ LA - en ID - AST_2012__346__1_0 ER -
%0 Book Section %A Gan, Wee Teck %A Gross, Benedict H. %A Prasad, Dipendra %T Symplectic local root numbers, central critical $L$-values, and restriction problems in the representation theory of classical groups %B Sur les Conjectures de Gross et Prasad. I %A Collectif %E Gan, W. T. %E Gross, B. H. %E Prasad, D. %E Waldspurger, J.-L. %S Astérisque %D 2012 %P 1-109 %N 346 %I Société mathématique de France %U http://www.numdam.org/item/AST_2012__346__1_0/ %G en %F AST_2012__346__1_0
Gan, Wee Teck; Gross, Benedict H.; Prasad, Dipendra. Symplectic local root numbers, central critical $L$-values, and restriction problems in the representation theory of classical groups, dans Sur les Conjectures de Gross et Prasad. I, Astérisque, no. 346 (2012), pp. 1-109. http://www.numdam.org/item/AST_2012__346__1_0/
[1] Genuine representations of the metaplectic group", Compositio Math. 113, p. 23-66. | DOI | MR | Zbl
and - "[2] Spherical pairs over close local fields", to appear in Comment. Math. Helvetici. | MR | Zbl
, and - "
[3] Multiplicity one theorem for
[4] Multiplicity one theorems", Annals of Math. 172 (2010), p. 1407-1434. | DOI | MR | Zbl
, , and - "[5] On some problems suggested by the trace formula", in Lie group representations, II (College Park, Md., 1982/1983)", Lecture Notes in Math., vol. 1041, Springer, 1984, p. 1-49. | MR | Zbl
- "[6] Unipotent automorphic representations: conjectures", Astérisque 171-172 (1989), p. 13-71. | Numdam | MR | Zbl
, "[7] Automorphic representations of classical groups", in preparation.
, "[8] The endoscopic classification of representations: orthogonal and symplectic groups", preprint. | MR | Zbl
, "[9] Degenerate principal series for even-orthogonal groups", Represent. Theory 7 (2003), p. 440-480. | DOI | MR | Zbl
and - "[10] Elements of Mathematics, Lie groups and Lie Algebras, Chapters 7-9, Springer, 2005. | MR | Zbl
-
[11] Canonical extensions of Harish-Chandra modules to representations of
[12] The unramified principal series of
[13] Les constantes des équations fonctionnelles des fonctions
[14] Les constantes locales de l'équation fonctionnelle de la fonction
[15] Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques", in Automorphic forms, representations and
[16] On the functional equation of the Artin
[17] Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence", to appear in Compositio Math.. | MR | Zbl
and - "
[18] The local Langlands conjecture for
[19] The local Langlands conjecture for
[20] Explicit constructions of automorphic
[21] On the nonvanishing of the central value of the Rankin-Selberg
[22] On the nonvanishing of the central value of the Rankin-Selberg
[23] Models for certain residual representations of unitary groups", AMS Contemp. Math. 488 (2009), p. 125-146. | DOI | MR | Zbl
, and , "
[24] On the decomposition of a representation of
[25] On irreducible representations of
[26] Arithmetic invariants of discrete Langlands parameters", Duke Math. J. 154 (2010), p. 431-508. | DOI | MR | Zbl
and - "
[27] Heegner points and derivatives of
[28] Theta dichotomy for unitary groups", J. Amer. Math. Soc. 9 (1996), p. 941-1004. | DOI | MR | Zbl
, and - "[29] The geometry and cohomology of some simple Shimura varieties, Annals of Math. Studies, vol. 151, Princeton Univ. Press, 2001. | MR | Zbl
and -[30] A refined Gross-Prasad conjecture for unitary groups", Ph.D. Thesis, University of California, San Diego, 2011. | MR
- "
[31] Une preuve simple des conjectures de Langlands pour
[32] Transcending classical invariant theory", J. Amer. Math. Soc. 2 (1989), p. 535-552. | DOI | MR | Zbl
- "[33] On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture", Geom. Funct. Anal. 19 (2010), p. 1378-1425. | DOI | MR | Zbl
and - "[34] Rankin-Selberg convolutions", Amer. J. Math. 105 (1983), p. 367-464. | DOI | MR | Zbl
, and - "[35] On the Gross-Prasad conjecture for unitary groups", Clay Math. Proc. 13 (2011), p. 205-264. | MR | Zbl
and - "[36] Rankin-Selberg convolutions: Archimedean theory", in Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part I (Ramat Aviv, 1989), Israel Math. Conf. Proc., vol. 2, Weizmann, 1990, p. 125-207. | MR | Zbl
and - "[37] Uniqueness of Bessel models: the archimedean case", Geom. and Funct. Anal. 20 (2010), p. 690-709. | DOI | MR | Zbl
, and - "[38] Whittaker-Shintani functions for orthogonal groups", Tohoku Math. J. 55 (2003), p. 1-64. | DOI | MR | Zbl
, and - "
[39] Multiplicity-one results and explicit formulas for quasi-split
[40] The book of involutions, AMS Colloquium Publ., vol. 44, 1998. | DOI | MR | Zbl
, , and -[41] Stable trace formula: elliptic singular terms", Math. Ann. 275 (1986), p. 365-399. | DOI | EuDML | MR | Zbl
- "[42] On the local theta-correspondence", Invent. Math. 83 (1986), p. 229-255. | DOI | EuDML | MR | Zbl
- "[43] Splitting metaplectic covers of dual reductive pairs", Israel J. Math. 87 (1994), p. 361-401. | DOI | MR | Zbl
, "
[44] On first occurrence in local theta correspondence", in Automorphic Representations,
[45] The Langlands conjecture for
[46]
[47] Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups", preprint arXiv: 1012.4538. | MR | Zbl
- "[48] Characteristic classes, Princeton Univ. Press, 1974, Annals of Mathematics Studies, No. 76. | MR | Zbl
and -
[49] Classification des séries discrètes pour certains groupes classiques
[50] Classification et changement de base pour les séries discrètes des groupes unitaires
[51] Correspondances de Howe sur un corps
[52] Spectral decomposition and Eisenstein series, Cambridge Tracts in Mathematics, vol. 113, Cambridge Univ. Press, 1995. | MR | Zbl
and -[53] La conjecture locale de Gross-Prasad pour les groupes spéciaux orthogonaux: le cas général", preprint.
and , "[54] Whittaker-Shintani functions on the symplectic group of Fourier-Jacobi type", Compositio Math. 79 (1991), p. 321-349. | EuDML | Numdam | MR | Zbl
and - "
[55] Shintani functions and automorphic
[56] Invariant forms for representations of
[57] On the local Howe duality correspondence", Internat. Math. Res. Notices (1993), p. 279-287. | DOI | MR | Zbl
, "[58] Theta correspondence for unitary groups", Pacific J. Math. 194 (2000), p. 427-438. | DOI | MR | Zbl
, "[59] On the Howe duality conjecture", Compositio Math. 51 (1984), p. 333-399. | EuDML | Numdam | MR | Zbl
- "[60] Automorphic representations of unitary groups in three variables", Annals of Mathematics Studies 123 (1990). | MR | Zbl
- "[61] Principe de densité pour les groupes réductifs", Compositio Math. 108 (1997), p. 151-184. | DOI | MR | Zbl
- "[62] A course in arithmetic, Grad. Texts in Math., vol. 7, Springer, 1973. | DOI | MR | Zbl
-[63] Linear algebraic groups, second éd., Progress in Math., vol. 9, Birkhäuser, 1998. | MR | Zbl
-[64] Multiplicity one theorems for symplectic groups", preprint arXiv:0903.1417. | Zbl
- "[65] Multiplicity one theorems: the Fourier-Jacobi models", to appear in Amer. J. of Math.. | MR | Zbl
, "[66] Multiplicity one theorems: the Archimedean case", Ann. of Math. 175 (2012), p. 23-44. | DOI | MR | Zbl
and - "[67] A note on special orthogonal groups following Waldspurger", preprint.
and , "[68] Functional equations of p-adic zeta integrals and representations of the metaplectic group", preprint, 1995.
- "
[69] Number theoretic background", in Automorphic forms, representations and
[70] The local Langlands conjecture", AMS Contemporary Mathematics 145 (1993), p. 305-379. | DOI | MR | Zbl
- "[71] Correspondance de Shimura", J. Math. Pures Appl. 59 (1980), p. 1-132. | MR | Zbl
- "
[72] Démonstration d'une conjecture de dualité de Howe dans le cas
[73] Correspondances de Shimura et quaternions", Forum Math. 3 (1991), p. 219-307. | EuDML | MR | Zbl
, "[74] Une formule intégrale reliée à la conjecture locale de Gross-Prasad", Comp. Math. 146 (2010), p. 1180-1290. | DOI | MR | Zbl
, "[75] Une formule intégrale reliée à la conjecture locale de Gross-Prasad, 2e partie: extension aux représentations tempérées", this volume, 2012. | Numdam | MR | Zbl
, "[76] Une variante d'un résultat de Aizenbud, Gourevitch, Rallis et Schiffmann", this volume, 2012. | Numdam | MR | Zbl
, "[77] Calcul d'une valeur d'un facteur epsilon par une formule intégrale", to appear in Astérisque. | Numdam | MR
, "[78] La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux", to appear in Astérisque. | Numdam | MR | Zbl
, "[79] On the constant term of a square integrable automorphic form", in Operator algebras and group representations, Vol. II (Neptun, 1980), Monogr. Stud. Math., vol. 18, Pitman, 1984, p. 227-237. | MR | Zbl
- "[80] Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press Inc., 1992. | MR | Zbl
,
[81]
[82] Basic number theory, third ed., Die Grund. Math. Wiss., vol. 144, Springer, 1974. | MR | Zbl
-[83] On the Siegel-Weil formula for quaternionic unitary groups", to appear in American J. of Math.. | MR | Zbl
- "[84] Heights of CM points I: Gross-Zagier formula", preprint available at https://wiki.epfl.ch/tan/documents/preprint(83%20pp)%202008%20yuan.pdf.
, and - "[85] Relative trace formula and arithmetic Gross-Prasad conjecture", preprint, 2009.
- "[86] Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups", preprint http://www.math.Columbia.edu/~wzhang/math/online/transfer.pdf, 2011. | MR
, "
[87] Theta dichotomy and doubling epsilon factors for