Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

• 成果类型: Article
• 署名作者: Badulescu, Alexandru Ioan
• 署名单位: Universite de Poitiers
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0104-8
• 发表日期: 2008
• 页码: 383-438
• 关键词: irreducible unitary representations; gl(n); characters; spectrum; THEOREM

摘要

In this paper we generalize the local Jacquet-Langlands correspondence to all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one Theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).