Functoriality for the classical groups
Cogdell, J. W. ; Kim, H. H. ; Piatetski-Shapiro, I. I. ; Shahidi, F.
Publications Mathématiques de l'IHÉS, Tome 99 (2004), p. 163-233 / Harvested from Numdam
@article{PMIHES_2004__99__163_0,
     author = {Cogdell, J. W. and Kim, H. H. and Piatetski-Shapiro, Ilya Iosifovich and Shahidi, F.},
     title = {Functoriality for the classical groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {99},
     year = {2004},
     pages = {163-233},
     doi = {10.1007/s10240-004-0020-z},
     mrnumber = {2075885},
     zbl = {1090.22010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_2004__99__163_0}
}
Cogdell, J. W.; Kim, H. H.; Piatetski-Shapiro, I. I.; Shahidi, F. Functoriality for the classical groups. Publications Mathématiques de l'IHÉS, Tome 99 (2004) pp. 163-233. doi : 10.1007/s10240-004-0020-z. http://gdmltest.u-ga.fr/item/PMIHES_2004__99__163_0/

1. J. Arthur, The principle of functoriality, Bull. Am. Math. Soc., 40 (2002), 39-53. | MR 1943132 | Zbl pre01832393

2. A. Borel, Automorphic L-functions, Proc. Symp. Pure Math., 33, part 2 (1979), 27-61. | MR 546608 | Zbl 0412.10017

3. N. Bourbaki, Algèbre Commutative, Ch. 3 et 4, Actualités Scientifiques et Industrielles, no. 1293. Hermann, Paris (1961).

4. W. Casselman and F. Shahidi, On reducibility of standard modules for generic representations, Ann. Sci. Éc. Norm. Supér., 31 (1998), 561-589. | Numdam | MR 1634020 | Zbl 0947.11022

5. J. W. Cogdell, Dual groups and Langlands Functoriality, An Introduction to the Langlands Program (J. Bernstein and S. Gelbart, eds.). Birkhäuser, Boston (2003), 251-268. | MR 1990382 | Zbl 1111.11314

6. J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to GLN, Publ. Math., Inst. Hautes Étud. Sci., 93 (2001), 5-30. | Numdam | MR 1863734 | Zbl 1028.11029

7. J. W. Cogdell and I. I. Piatetski-Shapiro, Converse Theorems for GLn , Publ. Math., Inst. Hautes Étud. Sci., 79 (1994), 157-214. | Numdam | MR 1307299 | Zbl 0814.11033

8. J. W. Cogdell and I. I. Piatetski-Shapiro, Stability of gamma factors for SO(2n+1), Manuscr. Math., 95 (1998), 437-461. | MR 1618194 | Zbl 0959.22011

9. J. W. Cogdell and I. I. Piatetski-Shapiro, Converse Theorems for GLn , II, J. Reine Angew. Math., 507 (1999), 165-188. | MR 1670207 | Zbl 0912.11022

10. J. W. Cogdell, I. I. Piatetski-Shapiro, and F. Shahidi, On stability of local γ-factors, in preparation.

11. S. Gelbart and H. Jacquet, A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. Éc. Norm. Supér., IV. Sér., 11 (1978), 471-542. | Numdam | MR 533066 | Zbl 0406.10022

12. S. Gelbart and F. Shahidi, Boundedness of automorphic L-functions in vertical strips, J. Am. Math. Soc., 14 (2001), 79-107. | MR 1800349 | Zbl 1050.11053

13. D. Ginzburg, S. Rallis, and D. Soudry, Generic automorphic forms on SO(2n+1): functorial lift to GL(2n), endoscopy, and base change, Int. Math. Res. Not., 2001, no. 14 (2001), 729-764. | MR 1846354 | Zbl 1060.11031

14. R. Godement and H. Jacquet, Zeta Functions of Simple Algebras, Lect. Notes Math., 260. Springer-Verlag, Berlin (1972). | MR 342495 | Zbl 0244.12011

15. M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. Math. Stud., 151. Princeton University Press, Princeton (2001). | MR 1876802 | Zbl 1036.11027

16. G. Henniart, Caractérisation de la correspondance de Langlands locale par les facteurs ε de paires, Invent. Math., 113 (1993), 339-350. | Zbl 0810.11069

17. G. Henniart, Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique, Invent. Math., 139 (2000), 439-455. | MR 1738446 | Zbl 1048.11092

18. R. Howe and I. I. Piatetski-Shapiro, A counter-example to the “generalized Ramanujan conjecture” for (quasi)-split groups, Proc. Symp. Pure Math., 33, part 1 (1979), 315-322. | Zbl 0423.22018

19. H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Conducteur des représentations du groupe linéaire., Math. Ann., 256 (1981), 199-214. | MR 620708 | Zbl 0443.22013

20. H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Rankin-Selberg convolutions, Am. J. Math., 105 (1983), 367-464. | MR 701565 | Zbl 0525.22018

21. H. Jacquet and J. Shalika, On Euler products and the classification of automorphic representations, Am. J. Math., 103 (1981), 499-558 and 777-815. | Zbl 0473.12008

22. H. Jacquet and J. Shalika, The Whittaker models for induced representations, Pac. J. Math., 109 (1983), 107-120. | MR 716292 | Zbl 0535.22017

23. H. Jacquet and J. Shalika, A lemma on highly ramified ε-factors, Math. Ann., 271 (1985), 319-332. | Zbl 0541.12010

24. C. Jantzen, On square integrable representations of classical p-adic groups, Can. J. Math., 52 (2000), 539-581. | MR 1758232 | Zbl 0995.22003

25. C. Jantzen, On square integrable representations of classical p-adic groups II, Represent. Theory, 4 (2000), 127-180. | MR 1789464 | Zbl 1045.22018

26. D. Jiang and D. Soudry, The local converse theorem for SO(2n+1) and applications, Ann. Math., 157 (2003), 743-806. | MR 1983781 | Zbl 1049.11055

27. D. Jiang and D. Soudry, Generic representations and local Langlands reciprocity law for p-adic SO2n+1, Contributions to Automorphic Forms, Geometry and Number Theory (Shalikafest 2002) (H. Hida, D. Ramakrishnan, and F. Shahidi, eds.). Johns Hopkins University Press, Baltimore, to appear. | MR 2058617 | Zbl 1062.11077

28. H. Kim, Langlands-Shahidi method and poles of automorphic L-functions, II, Isr. J. Math., 117 (2000), 261-284. | MR 1760595 | Zbl 1041.11035

29. H. Kim, Residual spectrum of odd orthogonal groups, Int. Math. Res. Not. 2001, no. 17 (2001), 873-906. | MR 1859343 | Zbl 1035.11020

30. H. Kim, Applications of Langlands' functoriality of odd orthogonal groups, Trans. Am. Math. Soc., 354 (2002), 2775-2796. | Zbl 1060.11033

31. H. Kim, On local L-functions and normalized intertwining operators, Can. J. Math., to appear. | MR 2134402 | Zbl 1096.11019

32. H. Kim and F. Shahidi, Functorial products for GL2×GL3 and the symmetric cube for GL2, Ann. Math., 155 (2002), 837-893. | MR 1923967 | Zbl 1040.11036

33. L. Lafforgue, Chtoucas de Drinfeld at correspondance de Langlands, Invent. Math., 147 (2002) 1-241. | MR 1875184 | Zbl 1038.11075

34. R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surv. Monogr., 31. Am. Math. Soc., Providence, RI (1989), 101-170. | MR 1011897 | Zbl 0741.22009

35. R. P. Langlands, Automorphic representations, Shimura varieties, and motives. Ein Märchen, Proc. Symp. Pure Math., 33, part 2 (1979), 205-246. | MR 546619 | Zbl 0447.12009

36. R. P. Langlands, Where stands functoriality today, Proc. Symp. Pure Math., 61 (1997), 457-471. | MR 1476510 | Zbl 0901.11032

37. W. Luo, Z. Rudnick, and P. Sarnak, On the generalized Ramanujan conjecture for GL(n), Proc. Symp. Pure Math., 66, part 2 (1999), 301-310. | MR 1703764 | Zbl 0965.11023

38. C. Moeglin, Points de réducibilité pour les induits de cuspidals, preprint (2001). | Zbl 1028.22016

39. C. Moeglin, Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc., 4 (2002), 141-200. | MR 1913095 | Zbl 1002.22009

40. C. Moeglin and M. Tadić, Construction of discrete series for p-adic classical groups, J. Am. Math. Soc., 15 (2002), 715-786. | MR 1896238 | Zbl 0992.22015

41. C. Moeglin and J-L. Waldspurger, Le spectre résiduel de GL(n), Ann. Sci. Éc. Norm. Supér., 22 (1989), 605-674. | Numdam | MR 1026752 | Zbl 0696.10023

42. G. Muić, On generic irreducible representations of Sp(n,F) and SO(2n+1,F), Glas. Mat., III. Ser., 33 (53) (1998), 19-31. | MR 1652772 | Zbl 0905.22009

43. G. Muić, Some results on square integrable representations; Irreducibility of standard representations, Int. Math. Res. Not., 1998, no. 14 (1998), 705-726. | MR 1637097 | Zbl 0909.22029

44. G. Muić, A proof of Casselman-Shahidi's conjecture for quasi-split classical groups, Can. Math. Bull., 44 (2001), 298-312. | Zbl 0984.22007

45. I. I. Piatetski-Shapiro, Multiplicity one theorems, Proc. Symp. Pure Math., 33, part 1 (1979), 209-212. | MR 546599 | Zbl 0423.22017

46. P. Sarnak, Estimates for Rankin-Selberg L-functions and quantum unique ergodicity, J. Funct. Anal., 184 (2001), 419-453. | MR 1851004 | Zbl 1006.11022

47. I. Satake, Theory of spherical functions on reductive algebraic groups over 𝔭-adic fields, Publ. Math., Inst. Hautes Étud. Sci., 18 (1963), 5-69. | Numdam | MR 195863 | Zbl 0122.28501

48. F. Shahidi, On certain L-functions, Am. J. Math., 103 (1981), 297-355. | MR 610479 | Zbl 0467.12013

49. F. Shahidi, Local coefficients as Artin factors for real groups, Duke Math. J., 52 (1985), 973-1007. | MR 816396 | Zbl 0674.10027

50. F. Shahidi, On the Ramanujan conjecture and finiteness of poles for certain L-functions, Ann. Math., 127 (1988), 547-584. | MR 942520 | Zbl 0654.10029

51. F. Shahidi, A proof of Langlands' conjecture on Plancherel measures; complementary series for p-adic groups, Ann. Math., 132 (1990), 273-330. | Zbl 0780.22005

52. F. Shahidi, On multiplicativity of local factors, Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, part II (Ramat Aviv, 1989), Israel Math. Conf. Proc., 3, Weizmann, Jerusalem (1990), 279-289. | MR 1159120 | Zbl 0841.11061

53. F. Shahidi, Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J., 66 (1992), 1-41. | MR 1159430 | Zbl 0785.22022

54. F. Shahidi, Twists of a general class of L-functions by highly ramified characters, Can. Math. Bull., 43 (2000), 380-384. | MR 1776066 | Zbl 1016.11016

55. F. Shahidi, Local coefficients as Mellin transforms of Bessel functions; Towards a general stability, Int. Math. Res. Not., 2002, no. 39 (2002), 2075-2119. | MR 1926651 | Zbl 1025.22014

56. D. Soudry, On Langlands functoriality from classical groups to GLn , Astérisque, to appear. | MR 2141707 | Zbl 1086.11025

57. R. Steinberg, Lectures on Chevalley Groups. Yale Lecture Notes, New Haven (1967). | MR 466335

58. M. Tadić, Classification of unitary representations in irreducible representations of general linear groups (non-Archimedean case), Ann. Sci. Éc. Norm. Supér., IV. Sér., 19 (1986), 335-382. | Numdam | MR 870688 | Zbl 0614.22005

59. J. Tate, Number theoretic background, Proc. Symp. Pure Math., 33, part 2 (1979), 3-26. | MR 546607 | Zbl 0422.12007

60. D. Vogan, Gelfand-Kirillov dimension for Harish-Chandra modules, Invent. Math., 48 (1978), 75-98. | MR 506503 | Zbl 0389.17002

61. A. Zelevinsky, Induced representations of reductive 𝔭-adic groups, II, Ann. Sci. Éc. Norm. Supér., 13 (1980), 165-210. | Numdam | MR 584084 | Zbl 0441.22014

62. Y. Zhang, The holomorphy and nonvanishing of normalized local intertwining operators, Pac. J. Math., 180 (1997), 386-398. | MR 1487571 | Zbl 1073.22502