On irreducibility of standard modules for generic representations
William Casselman; Freydoon Shahidi
Annales scientifiques de l'École Normale Supérieure (1998)
- Volume: 31, Issue: 4, page 561-589
- ISSN: 0012-9593
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topCasselman, William, and Shahidi, Freydoon. "On irreducibility of standard modules for generic representations." Annales scientifiques de l'École Normale Supérieure 31.4 (1998): 561-589. <http://eudml.org/doc/82470>.
@article{Casselman1998,
author = {Casselman, William, Shahidi, Freydoon},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {irreducibility of standard modules},
language = {eng},
number = {4},
pages = {561-589},
publisher = {Elsevier},
title = {On irreducibility of standard modules for generic representations},
url = {http://eudml.org/doc/82470},
volume = {31},
year = {1998},
}
TY - JOUR
AU - Casselman, William
AU - Shahidi, Freydoon
TI - On irreducibility of standard modules for generic representations
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1998
PB - Elsevier
VL - 31
IS - 4
SP - 561
EP - 589
LA - eng
KW - irreducibility of standard modules
UR - http://eudml.org/doc/82470
ER -
References
top- [1] J. ARTHUR, Intertwining operators and residues I. Weighted characters, (J. Funct. Anal., Vol. 84, 1989, pp. 19-84). Zbl0679.22011MR90j:22018
- [2] D. BARBASCH and A. MOY, Whittaker models with an Iwahori fixed vector, Representation theory and analysis on homogeneous spaces, (AMS, Rhode Island 1994, pp. 101-105). Zbl0854.22019MR95j:22024
- [3] I. N. BERNSTEIN and A. V. ZELEVINSKY, Induced representations of reductive p-adic groups I, (Ann. Scient. Éc. Norm. Sup., Vol. 10, 1977, pp. 441-472). Zbl0412.22015MR58 #28310
- [4] A. BOREL and N. WALLACH, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, (Annals of Math. Studies, Vol. 94, 1980, Princeton University Press, Princeton). Zbl0443.22010MR83c:22018
- [5] W. CASSELMAN, Introduction to the theory of admissible representations of p-adic reductive groups, preprint.
- [6] W. CASSELMAN, Canonical extensions of Harish-Chandra modules, (Cand. J. Math., Vol. 41, 1989, pp. 315-438). Zbl0702.22016MR90j:22013
- [7] W. CASSELMAN, Letter to Harish-Chandra, November 1982.
- [8] W. CASSELMAN and J.A. SHALIKA, The unramified principal series of p-adic groups II, The Whittaker function, (Comp. Math., Vol. 41, 1980, pp. 207-231). Zbl0472.22005MR83i:22027
- [9] J. W. COGDELL and I. I. PIATETSKI-SHAPIRO, Converse theorems for GLn, (Publ. Math. I.H.E.S., Vol. 79, 1994, pp. 157-214). Zbl0814.11033MR95m:22009
- [10] S. FRIEDBERG and D. GOLDBERG, On local coefficients for nongeneric representations of some classical groups, Comp. Math., to appear. Zbl0938.22018
- [11] S. GELBART, I. I. PIATETSKI-SHAPIRO, and S. RALLIS, Explicit construction of automorphic L-functions, (Lecture Notes in Math 1254, Springer-Verlag, 1987). Zbl0612.10022MR89k:11038
- [12] HARISH-CHANDRA, Harmonic analysis on real reductive groups III. The Maass-Selberg relations and the Plancherel formula, (Annals of Math., Vol. 104, 1976, pp. 117-201). Zbl0331.22007MR55 #12875
- [13] H. JACQUET and J. A. SHALIKA, Rankin Selberg Convolutions : Archimedean theory, in Festschrift in Honor of I.I. PIATETSKI-SHAPIRO, Part I, Editors : S. GELBART, R. HOWE, and P. SARNAK, (Israel Math. Conf. Proc., Vol. 2, Weizmann, Jerusalem, 1990, pp. 125-207). Zbl0712.22011MR93d:22022
- [14] H. JACQUET and J. A. SHALIKA, The Whittaker models for induced representations, (Pacific J. Math., Vol. 109, 1983, pp. 107-120). Zbl0535.22017MR85h:22023
- [15] H. KIM, Residual spectrum for Sp4, (Comp. Math., Vol. 99, 1995, pp. 129-151). Zbl0877.11030
- [16] A.W. KNAPP and E.M. STEIN, Intertwining operators for semisimple groups II, (Invent. Math., Vol. 60, 1980, pp. 9-84). Zbl0454.22010MR82a:22018
- [17] R. P. LANGLANDS, On the classification of irreducible representations of real algebraic groups, in (Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Editors P.J. SALLY, Jr. and D.A. VOGAN, Mathematical Surveys and Monographs, AMS, Vol. 31, 1989, pp. 101-170). Zbl0741.22009MR91e:22017
- [18] R. P. LANGLANDS, On Artin's L-functions, (Rice University Studies, Vol. 56, 1970, pp. 23-28). Zbl0245.12011
- [19] R. P. LANGLANDS, On the functional equations satisfied by Eisenstein series, (Lecture Notes in Math., Vol. 544, Springer-Verlag, 1976). Zbl0332.10018MR58 #28319
- [20] J.-S. LI, Some results on the unramified principal series of p-adic groups, (Math. Ann., Vol. 292, 1992, pp. 747-761). Zbl0804.22007MR93d:22023
- [21] C. MOEGLIN and J.-L. WALDSPURGER, Le spectre résiduel de GL(n), (Ann. Scient. Éc. Norm. Sup., Vol. 22, 1989, pp. 605-674). Zbl0696.10023MR91b:22028
- [22] M. REEDER, p-adic Whittaker functions and vector bundles on flag manifolds, (Comp. Math., Vol. 85, 1993, pp. 9-36). Zbl0819.22012MR93m:22020
- [23] F. SHAHIDI, A proof of Langlands' conjecture on Plancherel measures ; Complementary series for p-adic groups, (Ann. of Math., Vol. 132, 1990, pp. 273-330). Zbl0780.22005MR91m:11095
- [24] F. SHAHIDI, Local coefficients as Artin factors for real groups, (Duke Math. J., Vol. 52, 1985, pp. 973-1007). Zbl0674.10027MR87m:11049
- [25] F. SHAHIDI, On certain L-functions, (Amer. J. Math., Vol. 103, 1981, pp. 297-356). Zbl0467.12013MR82i:10030
- [26] F. SHAHIDI, On multiplicativity of local factors, in (Festschrift in Honor of I.I. Piatetski-Shapiro, Part II, Editors : S. GELBART, R. HOWE, and P. SARNAK, Israel Math. Conf. Proc., Vol. 3, Weizmann, Jerusalem, 1990, pp. 279-289). Zbl0841.11061MR93e:11144
- [27] F. SHAHIDI, Twisted endoscopy and reducibility of induced representations for p-adic groups, (Duke Math. J., Vol. 66, 1992, pp. 1-41). Zbl0785.22022MR93b:22034
- [28] A. SILBERGER, The Langlands quotient theorem for p-adic groups, (Math. Ann., Vol. 236, 1978, pp. 95-104). Zbl0362.20029MR58 #22413
- [29] A. SILBERGER, Introduction to Harmonic Analysis on Reductive p-adic Groups, Math. Notes of Princeton University Press, Vol. 23, Princeton, 1979. Zbl0458.22006MR81m:22025
- [30] D. SOUDRY, Rankin-Selberg convolutions for SO2l+1 × GLn : Local theory, preprint.
- [31] D. SOUDRY, On the archimedean theory of Rankin-Selberg Convolutions for SO2l+1 × GLn, (Ann. Scient. Éc. Norm. Sup., Vol. 28, 1995, pp. 161-224). Zbl0824.11034MR96m:11043
- [32] B. SPEH, Some results on principal series for GL(n, ℝ), Ph.D. Dissertation, (Massachusetts Institute of Technology, June, 1977).
- [33] B. SPEH and D. VOGAN, Reducibility of generalized principal series representations, (Acta Math., Vol. 145, 1980, pp. 227-299). Zbl0457.22011MR82c:22018
- [34] M. TADIĆ, On regular square integrable representations of p-adic groups, Amer. J. Math., Vol. 120, 1997, pp. 159-210. Zbl0903.22008MR99h:22026
- [35] M. TADIĆ, Construction of square integrable representations of classical p-adic groups, (Mathematica Gottingensis Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis, Heft, Vol. 11, 1993, pp. 1-48.20).
- [36] M. TADIĆ, Square integrable representations of classical p-adic groups of segment type, (Mathematica Gottingensis Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis, Heft, Vol. 15, 1994, pp. 1-16).
- [37] D. VOGAN, Gelfand-Kirillov dimension for Harish-Chandra modules, (Invent. Math., Vol. 48, 1978, pp. 75-98). Zbl0389.17002MR58 #22205
- [38] D. VOGAN, Unitarizability of certain series of representations, (Ann. of Math., Vol. 120, 1984, pp. 141-187). Zbl0561.22010MR86h:22028
- [39] D. VOGAN, Representations of real reductive Lie groups, Birkhauser, Boston, 1981. Zbl0469.22012MR83c:22022
- [40] N.R. WALLACH, Asymptotic expansions of generalized matrix entries of representations of real reductive groups, in (Lie Group Representations I, Lecture Notes in Math., Vol. 1024, Springer-Verlag, 1983, pp. 287-369). Zbl0553.22005MR85g:22029
- [41] A.V. ZELEVINSKY, Induced representations of reductive p-adic groups II, on irreducible representations of GL(n), (Ann. Scient. Éc. Norm. Sup., Vol. 13, 1980, pp. 165-210). Zbl0441.22014MR83g:22012
- [42] G. MUIĆ, Some results on square integrable representations ; Irreducibility of standard representations, preprint. Zbl0909.22029
- [43] Y. ZHANG, The holomorphy and nonvanishing of normalized local intertwining operators, (Pacific J. Math., Vol. 180, 1997, pp. 385-398). Zbl1073.22502MR98k:22076
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