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Soit un corps -adique de characteristique differente de . On caractérise la réducibilité des représentations de et qui sont induites paraboliquement par des représentations irréductibles. On donne aussi une classification (modulo les représentations cuspidales) de différentes classes de représentations irréductibles de ces groupes. Un cas spécial est la classification des représentations irréductibles unitaires.
Let be a -adic field whose characteristic is different from . The reducibilities of the representations of and which are parabolically induced by the irreducible representations are described. We obtain also classifications (modulo cuspidal representations) of various classes of irreducible representations of these groups. In particular, the classification of the irreducible unitary representations is obtained.
@incollection{MSMF_1993_2_52__75_0,
author = {Sally, Paul J. Jr. and Tadic, Marko},
title = {Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$},
booktitle = {Paires duales r\'eductives en caract\'eristiques 2. Induced representations and classifications for $GSp (2,F)$ and $Sp (2,F)$},
series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
pages = {75--133},
publisher = {Soci\'et\'e math\'ematique de France},
number = {52},
year = {1993},
doi = {10.24033/msmf.366},
mrnumber = {94e:22030},
zbl = {0784.22008},
url = {http://geodesic.mathdoc.fr/articles/10.24033/msmf.366/}
}
TY - CHAP AU - Sally, Paul J. Jr. AU - Tadic, Marko TI - Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$ BT - Paires duales réductives en caractéristiques 2. Induced representations and classifications for $GSp (2,F)$ and $Sp (2,F)$ AU - Collectif T3 - Mémoires de la Société Mathématique de France PY - 1993 SP - 75 EP - 133 IS - 52 PB - Société mathématique de France UR - http://geodesic.mathdoc.fr/articles/10.24033/msmf.366/ DO - 10.24033/msmf.366 ID - MSMF_1993_2_52__75_0 ER -
%0 Book Section %A Sally, Paul J. Jr. %A Tadic, Marko %T Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$ %B Paires duales réductives en caractéristiques 2. Induced representations and classifications for $GSp (2,F)$ and $Sp (2,F)$ %A Collectif %S Mémoires de la Société Mathématique de France %D 1993 %P 75-133 %N 52 %I Société mathématique de France %U http://geodesic.mathdoc.fr/articles/10.24033/msmf.366/ %R 10.24033/msmf.366 %F MSMF_1993_2_52__75_0
Sally, Paul J. Jr.; Tadic, Marko. Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$, dans Paires duales réductives en caractéristiques 2. Induced representations and classifications for $GSp (2,F)$ and $Sp (2,F)$, Mémoires de la Société Mathématique de France, Nouvelle série, no. 52 (1993), pp. 75-133. doi: 10.24033/msmf.366
[BZ] and , Induced representations of reductive p-adic groups I, Ann. Sci. École Norm Sup. 10 (1977), 441-472. | Zbl | MR | Numdam
[BWh] and , Continuous cohomology, discrete subgroups, and representations of reductive groups, Princeton University Press, Princeton, (1980). | Zbl | MR
[C] , Introduction to the theory of admissible representations of p-adic reductive groups, preprint.
[GeKn] and , L-indistinguishability and R groups for the special linear group, Advan. in Math., 43 (1982), 101-121. | Zbl | MR
[Gu] , The degenerate principal series for Sp(2n), Mem. of the Amer. Math. Society, 248 (1981), 1-81. | Zbl | MR
[HMr] and , Asymptotic properties of unitary representations, J. Functional Analysis, 32, No. 1 (1979), 72-96. | Zbl | MR
[J] , Degenerate principal series for symplectic groups, to appear in Mem. of the Amer. Math. Society. | Zbl
[Ke] , On the decomposition of reducible principal series representations of p-adic Chevalley groups, Pacific J. Math, 101 (1982), 351-388. | Zbl | MR
[Mi] , On C*-algebras with bounded trace, Glasnik Mat., 8(28) (1973), 7-21. | Zbl | MR
[Mo] , Representations of over a p-adic field : parts 1 and 2, Compositio Math., 66 (1988), 237-328. | Zbl | MR | Numdam
[R1] , Décomposition de la série principale des groupes réductifs p-adiques, Non-Commutative Harmonic Analysis, Lecture Notes in Math. 880, Springer-Verlag, Berlin (1981). | Zbl | MR
[R2] Sur les représentations non ramifiées des groupes réductifs p-adiques ; l'example de GSp(4), Bull. Soc. Math. France, 116 (1988), 15-42. | Zbl | MR | Numdam
[S1] , A proof of Langlands conjecture on Plancherel measures ; complementary series for p-adic groups, Ann. of Math., 132 (1990), 273-330. | Zbl | MR
[S2] , Langlands' conjecture on Plancherel measures of -adic groups, preprint.
[S3] , L-functions and representation theory of p-adic, preprint.
[S4] , Letter.
[T1] , Classification of unitary representations in irreducible representations of general linear group (non-archimedean case), Ann. Sci. École Norm. Sup, 19 (1986), 335-382. | Zbl | MR | Numdam
[T2] Induced representations of GL(n, A) for p-adic division algebras A, J. reine angew. Math., 405 (1990), 48-77. | Zbl | MR
[T3] , Notes on representations of non-archimedean SL(n), Pacific J. Math. (to appear).
[T4] , Representations of p-adic symplectic groups, preprint.
[T5] , On Jaquet modules of induced representations of p-adic symplectic groups, preprint.
[T6] , A structure arising from induction and restriction of representations of classical p-adic groups, preprint.
[T7] , Representations of classical p-adic groups, preprint.
[Wd] , Un exercice sur et les représentations de Weil, Bull. Soc. Math. France, 115 (1987), 35-69. | Zbl | MR | Numdam
[Z1] , Induced representations of reductive -adic groups II, On irreducible representations of , Ann. Sci École Norm Sup., 13 (1980), 165-210. | Zbl | MR | Numdam
[Z2] , Representations of Finite Classical Groups, A Hopf Algebra Approach, Lecture Notes in Math 869, Springer-Verlag, Berlin, (1981). | Zbl | MR
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