Voir la notice de l'article provenant de la source Annals of Mathematics website
Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by M\oe glin and for the exceptional Chevalley group $G_2$ by Kim. In this paper we extend their results on spherical representations to the remaining exceptional groups $E_6$, $E_7$, $E_8$, and $F_4$. In particular, we prove Arthur’s conjecture that the spherical constituent of an unramified principal series of a Chevalley group over any local field of characteristic zero is unitarizable if its Langlands parameter coincides with half the weighted marking of a coadjoint nilpotent orbit of the Langlands dual Lie algebra.
@article{10_4007_annals_2013_177_3_9,
author = {Stephen D. Miller},
title = {Residual automorphic forms and spherical unitary representations of exceptional groups},
journal = {Annals of mathematics},
pages = {1169--1179},
publisher = {mathdoc},
volume = {177},
number = {3},
year = {2013},
doi = {10.4007/annals.2013.177.3.9},
mrnumber = {3034297},
zbl = {1269.22009},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.9/}
}
TY - JOUR AU - Stephen D. Miller TI - Residual automorphic forms and spherical unitary representations of exceptional groups JO - Annals of mathematics PY - 2013 SP - 1169 EP - 1179 VL - 177 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.9/ DO - 10.4007/annals.2013.177.3.9 LA - en ID - 10_4007_annals_2013_177_3_9 ER -
%0 Journal Article %A Stephen D. Miller %T Residual automorphic forms and spherical unitary representations of exceptional groups %J Annals of mathematics %D 2013 %P 1169-1179 %V 177 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.9/ %R 10.4007/annals.2013.177.3.9 %G en %F 10_4007_annals_2013_177_3_9
Stephen D. Miller. Residual automorphic forms and spherical unitary representations of exceptional groups. Annals of mathematics, Tome 177 (2013) no. 3, pp. 1169-1179. doi: 10.4007/annals.2013.177.3.9
Cité par Sources :