标题： 剩余自守形式与例外群的球面酉表示 显示英文标题

标题： Residual automorphic forms and spherical unitary representations of exceptional groups

摘要： 阿瑟推测，可以通过找到适当的自守实现来证明若干表示的酉性。莫格林已验证了经典群的情况，金验证了例外李群G_2的情况。本文将他们的球面表示的结果推广到剩余的例外群E_6、E_7、E_8和F_4。特别是，我们证明了阿瑟的猜想：任意特征零局部域上的Chevalley群的非分歧主级数的球面组成分，在其Langlands参数与Langlands对偶李代数的余伴随幂零轨道标记的一半相同时，是可酉化的。 显示英文摘要

摘要： 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.