On lifting from classical groups to
J. W. Cogdell; H. H. Kim; I. I. Piatetski-Shapiro; F. Shahidi
Publications Mathématiques de l'IHÉS (2001)
- Volume: 93, page 5-30
- ISSN: 0073-8301
Access Full Article
topHow to cite
topCogdell, J. W., et al. "On lifting from classical groups to $GL_N$." Publications Mathématiques de l'IHÉS 93 (2001): 5-30. <http://eudml.org/doc/104177>.
@article{Cogdell2001,
author = {Cogdell, J. W., Kim, H. H., Piatetski-Shapiro, I. I., Shahidi, F.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Langlands functorial lift; ; ; generic cuspidal automorphic representations; weak functorial lift},
language = {eng},
pages = {5-30},
publisher = {Institut des Hautes Etudes Scientifiques},
title = {On lifting from classical groups to $GL_N$},
url = {http://eudml.org/doc/104177},
volume = {93},
year = {2001},
}
TY - JOUR
AU - Cogdell, J. W.
AU - Kim, H. H.
AU - Piatetski-Shapiro, I. I.
AU - Shahidi, F.
TI - On lifting from classical groups to $GL_N$
JO - Publications Mathématiques de l'IHÉS
PY - 2001
PB - Institut des Hautes Etudes Scientifiques
VL - 93
SP - 5
EP - 30
LA - eng
KW - Langlands functorial lift; ; ; generic cuspidal automorphic representations; weak functorial lift
UR - http://eudml.org/doc/104177
ER -
References
top- [1] D. BARBASCH and A. MOY, Whittaker models with an Iwahori fixed vector, Contemporary Mathematics 177 (1994), 101-105. Zbl0854.22019MR1303602
- [2] A. BOREL, Automorphic L-functions, Proc. Symp. Pure Math. 33, part 2 (1979), 27-61. Zbl0412.10017MR546608
- [3] W. CASSELMAN and F. SHAHIDI, On reducibility of standard modules for generic representations, Ann. Sci. École Norm. Sup. 31 (1998), 561-589. Zbl0947.11022MR1634020
- [4] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Converse theorems for GLn, Publ. Math. IHES 79 (1994), 157-214. Zbl0814.11033MR1307299
- [5] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Unitarity and functoriality, Geom. Funct. Anal. 5 (1995), 164-173. Zbl0842.11021MR1334866
- [6] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Stability of gamma factors for SO(2n + 1), Manuscripta math. 95 (1998), 437-461. Zbl0959.22011MR1618194
- [7] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Converse theorems for GLn, II, J. reine angew. Math. 507 (1999), 165-188. Zbl0912.11022MR1670207
- [8] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Converse theorems for GLn and their application to liftings, to appear in the proceedings of the International Conference on Cohomology of Arithmetic Groups, Automorphic Forms, and L-functions, Tata Institute of Fundamental Research. Zbl1039.11030MR1986092
- [9] S. GELBART and I. I. PIATETSKI-SHAPIRO, L-functions for G × GLn, Springer Lecture Notes in Math. 1254, 52-146.
- [10] S. GELBART and F. SHAHIDI, Boundedness of automorphic L-functions in finite vertical strips, to appear, Journal of the AMS. Zbl1050.11053
- [11] D. GINZBURG, L-functions for SOn × GLk, J. reine angew. Math. 405 (1990), 156-280. Zbl0684.22009MR1041001
- [12] G. HENNIART, Caractérisation de la correspondance de Langlands locale par les facteurs de paires, Invent. Math. 113 (1993), 339-350. Zbl0810.11069MR1228128
- [13] H. JACQUET, I. I. PIATETSKI-SHAPIRO and J. SHALIKA, Rankin-Selberg convolutions, Am. J. Math. 105 (1983), 367-464. Zbl0525.22018MR701565
- [14] H. JACQUET and J. SHALIKA, On Euler products and the classification of automorphic representations, I, Am. J. Math. 103 (1981), 499-558; II, 103 (1981), 777-815. Zbl0473.12008MR618323
- [15] H. JACQUET and J. SHALIKA, The Whittaker models for induced representations, Pacific J. Math. 109 (1983), 107-120. Zbl0535.22017MR716292
- [16] H. JACQUET and J. SHALIKA, A lemma on highly ramified -factors, Math. Ann. 271 (1985), 319-332. Zbl0541.12010MR787183
- [17] H. JACQUET and J. SHALIKA, Rankin-Selberg Convolutions: Archimedean Theory, Festschrift in Honor of I. I. Piatetski-Shapiro, Part I, Jerusalem, Weizmann Science Press (1990), 125-207. Zbl0712.22011MR1159102
- [18] H. KIM, Langlands-Shahidi method and poles of automorphic L-functions: Applications to exterior square L-functions, Canad. J. Math. 51 (1999), 835-849. Zbl0934.11024MR1701344
- [19] H. KIM, Langlands-Shahidi method and poles of automorphic L-functions, II, Israel J. Math. 117 (2000), 261-284; Correction, Israel J. Math. 118 (2000), 379. Zbl1041.11035MR1760595
- [20] R. P. LANGLANDS, Problems in the theory of automorphic forms, Lectures in Modern Analysis and Applications, III, Lecture Notes in Math. 170, Springer Verlag, Berlin (1970), 18-61. Zbl0225.14022MR302614
- [21] R. P. LANGLANDS, On the Functional Equations Satisfied by Eisenstein Series, Lecture Notes in Mathematics 544, Springer Verlag, Berlin (1976). Zbl0332.10018MR579181
- [22] R. P. LANGLANDS, On the notion of an automorphic representation, Proc. Sympos. Pure Math. 33, part 1 (1979) 189-207. Zbl0414.22021MR546598
- [23] R. P. LANGLANDS, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surveys Monographs, 31, Amer. Math. Soc. Providence, RI (1989), 101-170. Zbl0741.22009MR1011897
- [24] J.-S. LI, Some remarks on unramified principal series of p-adic groups, Math. Ann. 292 (1992), 747-761. Zbl0804.22007MR1157324
- [25] G. LUSZTIG, Representations of affine Hecke algebras, Astérisque 171-172 (1989), 73-84. Zbl0699.22027MR1021500
- [26] C. MOEGLIN and J.-L. WALDSPURGER, Spectral decomposition and Eisenstein series. Une paraphrase de l’Écriture, Cambridge Tracts in Mathematics, 113, Cambridge, Cambridge University Press (1995). Zbl0846.11032
- [27] G. MUIĆ, Some results on square integrable representations; Irreducibility of standard representations, IMRN No. 14 (1998), 705-726. Zbl0909.22029MR1637097
- [28] M. REEDER, p-adic Whittaker functions and vector bundles on flag manifolds, Compositio Math. 85 (1993), 9-36. Zbl0819.22012MR1199202
- [29] I. SATAKE, Theory of spherical functions on reductive algebraic groups over p-adic fields, Publ. Math. IHES 18 (1963), 5-69. Zbl0122.28501MR195863
- [30] F. SHAHIDI, Local coefficients as Artin factors for real groups, Duke Math. J. 52 (1985), 973-1007. Zbl0674.10027MR816396
- [31] F. SHAHIDI, A proof of Langlands’ conjecture on Plancherel measures; complementary series for p-adic groups, Ann. of Math. 132 (1990), 273-330. Zbl0780.22005
- [32] 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. Zbl0841.11061MR1159120
- [33] F. SHAHIDI, Twists of a general class of L-functions by highly ramified characters, Canad. Math. Bull. 43 (2000), 380-384. Zbl1016.11016MR1776066
- [34] D. SOUDRY, Rankin-Selberg convolutions for SO2l+1 × GLn; Local theory, Memoirs of the AMS 500 (1993). Zbl0805.22007
- [35] D. SOUDRY, On the Archimedean Theory of Rankin-Selberg convolutions for SO2l+1 × GLn, Ann. scient. Éc. Norm. Sup. 28 (1995), 161-224. Zbl0824.11034MR1318068
- [36] D. SOUDRY, Full multiplicativity of gamma factors for SO2l+1 × GLn, preprint. Zbl1005.11027
- [37] J. TATE, Number theoretic background, Proc. Symp. Pure Math. 33 (1979), 3-26. Zbl0422.12007MR546607
- [38] H. YOSHIDA, On the unitarizability of principal series representations of p-adic Chevalley groups, J. Math. Kyoto Univ. 32 (1992), 155-233. Zbl0794.22016MR1145650
- [39] A. ZELEVINSKY, Induced representations of reductive p-adic groups II, Ann. Sci. École Norm. Sup. 13 (1980), 165-210. Zbl0441.22014MR584084
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.