Geodesic
Residual automorphic forms and spherical unitary representations of exceptional groups
Stephen D. Miller1
1 Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019
Annals of mathematics, Tome 177 (2013) no. 3, pp. 1169-1179.

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.
DOI : 10.4007/annals.2013.177.3.9

Stephen D. Miller 1

1 Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019 
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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. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.3.9/

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