Residual automorphic forms and spherical unitary representations of exceptional groups

• 成果类型: Article
• 署名作者: Miller, Stephen D.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.3.9
• 发表日期: 2013
• 页码: 1169-1179
• 关键词: spectrum

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 Lang lands parameter coincides with half the weighted marking of a coadjoint nilpotent orbit of the Lang lands dual Lie algebra.