Geometric structure in the representation theory of <i>p</i>-adic groups

Anne-Marie Aubert; Paul Baum; Roger Plymen

doi:10.1016/j.crma.2007.10.011

Harmonic Analysis

Geometric structure in the representation theory of p-adic groups
[Structure géométrique en théorie des représentations des groupes p-adiques]

Présenté par : Alain Connes

Anne-Marie Aubert ¹ ; Paul Baum ² ; Roger Plymen ³

¹ Institut de Mathématiques de Jussieu, U.M.R. 7586 du C.N.R.S., 175, rue du Chevaleret, 75013 Paris, France
² Pennsylvania State University, Mathematics Department, University Park, PA 16802, USA
³ School of Mathematics, Manchester University, Manchester M13 9PL, UK

Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 573-578.

Résumé
Abstract

Nous conjecturons l'existence d'une structure géométrique simple sous-jacente aux questions de réductibilité des représentations induites paraboliques des groupes réductifs p-adiques.

We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.

Reçu le : 2006-07-17
Accepté le : 2007-10-02
Publié le : 2007-11-07

DOI : 10.1016/j.crma.2007.10.011

Affiliations des auteurs :

Anne-Marie Aubert ¹ ; Paul Baum ² ; Roger Plymen ³

¹ Institut de Mathématiques de Jussieu, U.M.R. 7586 du C.N.R.S., 175, rue du Chevaleret, 75013 Paris, France
² Pennsylvania State University, Mathematics Department, University Park, PA 16802, USA
³ School of Mathematics, Manchester University, Manchester M13 9PL, UK

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     title = {Geometric structure in the representation theory of \protect\emph{p}-adic groups},
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     pages = {573--578},
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     number = {10},
     year = {2007},
     doi = {10.1016/j.crma.2007.10.011},
     language = {en},
}

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Anne-Marie Aubert; Paul Baum; Roger Plymen. Geometric structure in the representation theory of p-adic groups. Comptes Rendus. Mathématique, Volume 345 (2007) no. 10, pp. 573-578. doi : 10.1016/j.crma.2007.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.10.011/

Bibliographie
Cité par

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[2] A.-M. Aubert; P. Baum; R.J. Plymen The Hecke algebra of a reductive p-adic group: a geometric conjecture (C. Consani; M. Marcolli, eds.), Noncommutative Geometry and Number Theory, Aspects of Mathematics, vol. 37, Vieweg Verlag, 2006, pp. 1-34

[3] A.-M. Aubert, P. Baum, R.J. Plymen, Geometric structure in the principal series of the p-adic group $G_{2}$ , preprint, 2007

[4] P. Baum; A. Connes The Chern character for discrete groups, A Fête of Topology, Academic Press, New York, 1988, pp. 163-232

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[7] J. Brodzki; R.J. Plymen Complex structure on the smooth dual of $GL (n)$ , Documenta Math., Volume 7 (2002), pp. 91-112

[8] D. Eisenbud; J. Harris The Geometry of Schemes, Springer, 2001

[9] M. Harris; R. Taylor The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. of Math. Stud., vol. 151, Princeton, 2001

[10] G. Muić The unitary dual of p-adic $G_{2}$ , Duke Math. J., Volume 90 (1997), pp. 465-493

[11] A. Ram Representations of rank two affine Hecke algebras (C. Musili, ed.), Advances in Algebra and Geometry, Hindustan Book Agency, 2003, pp. 57-91

[12] J.-L. Waldspurger La formule de Plancherel pour les groupes p-adiques d'après Harish-Chandra, J. Inst. Math. Jussieu, Volume 2 (2003), pp. 235-333

[13] A.V. Zelevinsky Induced representations of reductive p-adic groups II, Ann. Sci. École Norm. Sup., Volume 13 (1980), pp. 154-210

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