Multiplicity one theorems

• 成果类型: Article
• 署名作者: Aizenbud, Avraham; Gourevitch, Dmitry; Rallis, Stephen; Schiffmann, Gerard
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1407-1434
• 关键词: shintani functions; gelfand pair; REPRESENTATIONS; DECOMPOSITION; gl(2)

摘要

In the local, characteristic 0, non-Archimedean case, we consider distributions on GL(n + 1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL(n + 1) to GL(n). Similar theorems are obtained for orthogonal or unitary groups.