Geodesic
Discrete Series of Classical Groups
Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 1101-1120

Voir la notice de l'article provenant de la source Cambridge University Press

Let ${{G}_{n}}$ be the split classical groups $\text{Sp}(\text{2}n\text{),}\,\text{SO(2}n\text{+1})$ and $\text{SO(2}n\text{)}$ defined over a $p$ -adic field F or the quasi-split classical groups $U(n,n)$ and $U(n+1,n)$ with respect to a quadratic extension $E/F$ . We prove the self-duality of unitary supercuspidal data of standard Levi subgroups of ${{G}_{n}}(F)$ which give discrete series representations of ${{G}_{n}}(F)$ .
DOI : 10.4153/CJM-2000-046-7
Mots-clés : 22E35 
Zhang, Yuanli. Discrete Series of Classical Groups. Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 1101-1120. doi: 10.4153/CJM-2000-046-7
@article{10_4153_CJM_2000_046_7,
     author = {Zhang, Yuanli},
     title = {Discrete {Series} of {Classical} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1101--1120},
     year = {2000},
     volume = {52},
     number = {5},
     doi = {10.4153/CJM-2000-046-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-046-7/}
}
TY  - JOUR
AU  - Zhang, Yuanli
TI  - Discrete Series of Classical Groups
JO  - Canadian journal of mathematics
PY  - 2000
SP  - 1101
EP  - 1120
VL  - 52
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-046-7/
DO  - 10.4153/CJM-2000-046-7
ID  - 10_4153_CJM_2000_046_7
ER  - 
%0 Journal Article
%A Zhang, Yuanli
%T Discrete Series of Classical Groups
%J Canadian journal of mathematics
%D 2000
%P 1101-1120
%V 52
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-046-7/
%R 10.4153/CJM-2000-046-7
%F 10_4153_CJM_2000_046_7

[1] [1] Ban, D., Self-duality in the Case of SO(2n, F). Preprint. Google Scholar

[2] [2] Bourbaki, N., Éléments de mathématique. Fasc. 52XIV, Groupes et algébres de Lie. Chapitres IV, V, VI. Actualit és Scientifiques et Industrielles 1337, Hermann, Paris, 1968. Google Scholar

[3] [3] Casselman, W., Introduction to the Theory of Admissible Representations of p-adic Reductive Groups. Preprint. Google Scholar

[4] [4] Casselman, W. and Shahidi, F., Irreducibility of StandardModules for Generic Representations. Ann. Sci. École Norm. Sup. 31(1998), 561–589. Google Scholar

[5] [5] Goldberg, D., Reducibility of Induced Representations for Sp(2N) and SO(N). Amer. J. Math. 116(1994), 1101–1151. Google Scholar

[6] [6] Jantzen, C., On Square-integrable Representations of Classical p-adic Groups. Preprint. Google Scholar

[7] [7] Jacquet, H., Piateski-Shapiro, I. and Shalika, J., Rankin-Selberg Convolutions. Amer. J. Math. 105(1983), 367–464. Google Scholar

[8] [8] Muić, G., Some results on square Integrable Representations; Irreducibility of Standard Representations. Internat. Math. Res. Notices 14(1998), 705–726. Google Scholar

[9] [9] Shahidi, F., A Proof of Langlands’ Conjecture on PlancherelMeasures; Complementary Series for p-adic Groups. Ann. of Math. 132(1990), 273–330. Google Scholar

[10] [10] Shahidi, F., On multiplicativity of local factors. In: Festschrift in Honor of I. I. Piateski-Shapiro, Part II, Israel Math. Conf. Proc. 3, Weizmann, Jerusalem, 1990, 279–289. Google Scholar

[11] [11] Silberger, A., Introduction to Harmonic Analysis on p-Adic Groups. Math. Notes 23, Princeton University Press, Princeton, 1979. Google Scholar

[12] [12] Silberger, A., Special Representations of Reductive p-Adic Groups are not integrable. Ann. of Math. 111(1980), 571–587. Google Scholar

[13] [13] Silberger, A., Discrete Series of and Classification for p-adic Groups I. Amer. J. Math. (6) 103(1981), 1241–1321. Google Scholar

[14] [14] Tadic, M., On Regular Square Integrable Representations of p-Adic Groups. Amer. J. Math. 120(1998), 159–210. Google Scholar

[15] [15] Zhang, Z., L-packets and Reducibilities. J. Reine Angew. Math. 510(1999), 83–102. Google Scholar

Cité par Sources :