Multiplicity one theorems: the Archimedean case

• 成果类型: Article
• 署名作者: Sun, Binyong; Zhu, Chen-Bo
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.1.2
• 发表日期: 2012
• 页码: 23-44
• 关键词: local-field f; gelfand pair

摘要

Let G be one of the classical Lie groups GL(n+1)(R), GL(n+1)(C), U(p, q + 1), O(p, q + 1), On+1(C), SO(p, q + 1), SOn+1(C), and let G' be respectively the subgroup GL(n)(R), GL(n)(C), U(p, q), O(p, q), O-n(C), SO(p, q), SO (C), embedded in G in the standard way. We show that every irreducible Casselman-Wallach representation of G' occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of G. Similar results are proved for the Jacobi groups GL(n)(R) (sic) H2n+1(R), GL(n)(C) (sic) H2n+1 (C), U(p, q) (sic) H2p+2q+1(R), Sp(2n)(R) (sic) H2n+1(R), Sp(2n)(C) (sic) H2n+1 (C) with their respective subgroups GL(n)(R), GL(n)(C), U(p, q), Sp(2n)(R), and SP2n(C).