  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 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 marking of a coadjoint nilpotent orbit of the Langlands dual Lie
algebra.
