[Formule de Plancherel explicite pour le groupe p-adique GL(n)]
Nous obtenons une formule de Plancherel explicite pour le groupe p-adique GL(n). Nous déterminons explicitement la décomposition de Bernstein de la mesure de Plancherel, y compris les diverses constantes numériques. Nous prouvons aussi une formule de transfert pour GL(n).
We provide an explicit Plancherel formula for the p-adic group GL(n). We determine explicitly the Bernstein decomposition of Plancherel measure, including all numerical constants. We also prove a transfer-of-measure formula for GL(n).
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@article{CRMATH_2004__338_11_843_0,
author = {Aubert, Anne-Marie and Plymen, Roger},
title = {Explicit {Plancherel} formula for the \protect\emph{p}-adic group {GL(\protect\emph{n})}},
journal = {Comptes Rendus. Math\'ematique},
pages = {843--848},
publisher = {Elsevier},
volume = {338},
number = {11},
year = {2004},
doi = {10.1016/j.crma.2004.03.026},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.03.026/}
}
TY - JOUR AU - Aubert, Anne-Marie AU - Plymen, Roger TI - Explicit Plancherel formula for the p-adic group GL(n) JO - Comptes Rendus. Mathématique PY - 2004 SP - 843 EP - 848 VL - 338 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.03.026/ DO - 10.1016/j.crma.2004.03.026 LA - en ID - CRMATH_2004__338_11_843_0 ER -
%0 Journal Article %A Aubert, Anne-Marie %A Plymen, Roger %T Explicit Plancherel formula for the p-adic group GL(n) %J Comptes Rendus. Mathématique %D 2004 %P 843-848 %V 338 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.03.026/ %R 10.1016/j.crma.2004.03.026 %G en %F CRMATH_2004__338_11_843_0
Aubert, Anne-Marie; Plymen, Roger. Explicit Plancherel formula for the p-adic group GL(n). Comptes Rendus. Mathématique, Tome 338 (2004) no. 11, pp. 843-848. doi : 10.1016/j.crma.2004.03.026. http://www.numdam.org/articles/10.1016/j.crma.2004.03.026/
[1] A.-M. Aubert, R.J. Plymen, Plancherel measure for GL(n): explicit formulas and Bernstein decomposition, Preprint, 2004
[2] Representations of p-adic groups, Harvard University, 1992 (Notes by K.E. Rumelhart)
[3] Local Rankin–Selberg convolutions for GLn: explicit conductor formula, J. Amer. Math. Soc., Volume 11 (1998), pp. 703-730
[4] C.J. Bushnell, G. Henniart, P.C. Kutzko, Towards an explicit Plancherel theorem for reductive p-adic groups, Preprint, 2001
[5] The Admissible Dual of GL(n) via Compact Open Subgroups, Ann. of Math. Stud., vol. 129, Princeton University Press, Princeton, NJ, 1993
[6] Smooth representations of reductive p-adic groups: structure theory via types, Proc. London Math. Soc., Volume 77 (1998), pp. 582-634
[7] The local Langlands correspondence, Proc. Symp. Pure Math., Volume 55 (1994), pp. 365-391
[8] Harmonic analysis on semi-simple groups, Actes Congr. Internat. Math., Tome 2, Nice, 1970, 1971, pp. 331-335
[9] Reduced -algebra of the p-adic group GL(n) II, J. Funct. Anal., Volume 196 (2002), pp. 119-134
[10] A proof of Langlands conjecture on Plancherel measure; complementary series for p-adic groups, Ann. of Math., Volume 132 (1990), pp. 273-330
[11] Langlands' conjecture on Plancherel measures for p-adic groups, Harmonic Analysis on Reductive Groups, Brunswick, ME, 1989, Progr. Math., vol. 101, Birkhäuser Boston, Boston, MA, 1991, pp. 277-295
[12] La formule de Plancherel 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. 165-210
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