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 Cheval- ley 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 constituentof 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty