Resumen de Residual automorphic forms and spherical unitary representations of exceptional groups

Stephen D. Miller

• 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