Residual automorphic forms and spherical unitary representations of exceptional groups

Abstract 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 Moeglin and for the exceptional Chevalley group G2 by Kim. In this paper we extend their results on spherical representations to the remaining exceptional groups E6, E7, E8, and F4. 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