We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.
Nous conjecturons l'existence d'une structure géométrique simple sous-jacente aux questions de réductibilité des représentations induites paraboliques des groupes réductifs p-adiques.
Accepted:
Published online:
@article{CRMATH_2007__345_10_573_0, author = {Aubert, Anne-Marie and Baum, Paul and Plymen, Roger}, title = {Geometric structure in the representation theory of \protect\emph{p}-adic groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {573--578}, publisher = {Elsevier}, volume = {345}, number = {10}, year = {2007}, doi = {10.1016/j.crma.2007.10.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.011/} }
TY - JOUR AU - Aubert, Anne-Marie AU - Baum, Paul AU - Plymen, Roger TI - Geometric structure in the representation theory of p-adic groups JO - Comptes Rendus. Mathématique PY - 2007 SP - 573 EP - 578 VL - 345 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.011/ DO - 10.1016/j.crma.2007.10.011 LA - en ID - CRMATH_2007__345_10_573_0 ER -
%0 Journal Article %A Aubert, Anne-Marie %A Baum, Paul %A Plymen, Roger %T Geometric structure in the representation theory of p-adic groups %J Comptes Rendus. Mathématique %D 2007 %P 573-578 %V 345 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.011/ %R 10.1016/j.crma.2007.10.011 %G en %F CRMATH_2007__345_10_573_0
Aubert, Anne-Marie; Baum, Paul; Plymen, Roger. 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. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.011/
[1] Plancherel measure for and : Explicit formulas and Bernstein decomposition, J. Number Theory, Volume 112 (2005), pp. 26-66
[2] The Hecke algebra of a reductive p-adic group: a geometric conjecture (Consani, C.; Marcolli, M., 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 , preprint, 2007
[4] The Chern character for discrete groups, A Fête of Topology, Academic Press, New York, 1988, pp. 163-232
[5] Representations of p-Adic Groups, Notes by K.E. Rumelhart, Harvard University, 1992
[6] Induced representations of reductive p-adic groups I, Ann. Sci. E.N.S., Volume 4 (1977), pp. 441-472
[7] Complex structure on the smooth dual of , Documenta Math., Volume 7 (2002), pp. 91-112
[8] The Geometry of Schemes, Springer, 2001
[9] The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. of Math. Stud., vol. 151, Princeton, 2001
[10] The unitary dual of p-adic , Duke Math. J., Volume 90 (1997), pp. 465-493
[11] Representations of rank two affine Hecke algebras (Musili, C., ed.), Advances in Algebra and Geometry, Hindustan Book Agency, 2003, pp. 57-91
[12] La formule de Plancherel pour les groupes p-adiques d'après Harish-Chandra, J. Inst. Math. Jussieu, Volume 2 (2003), pp. 235-333
[13] Induced representations of reductive p-adic groups II, Ann. Sci. École Norm. Sup., Volume 13 (1980), pp. 154-210
Cited by Sources: