Comptes Rendus
no. 10
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 Aubert1 ; Paul Baum2 ; Roger Plymen3
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.10.011
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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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/

[1] A.-M. Aubert; R.J. Plymen Plancherel measure for GL(n,F) and GL(m,D): Explicit formulas and Bernstein decomposition, J. Number Theory, Volume 112 (2005), pp. 26-66

[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 G2, preprint, 2007

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[5] J. Bernstein Representations of p-Adic Groups, Notes by K.E. Rumelhart, Harvard University, 1992

[6] I.N. Bernstein; A.V. Zelevinsky Induced representations of reductive p-adic groups I, Ann. Sci. E.N.S., Volume 4 (1977), pp. 441-472

[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 G2, 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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