Please use this identifier to cite or link to this item: https://doi.org/10.4007/annals.2012.175.1.2
Title: Multiplicity one theorems: The Archimedean case
Authors: Sun, B.
Zhu, C.-B. 
Issue Date: Jan-2012
Citation: Sun, B., Zhu, C.-B. (2012-01). Multiplicity one theorems: The Archimedean case. Annals of Mathematics 175 (1) : 23-44. ScholarBank@NUS Repository. https://doi.org/10.4007/annals.2012.175.1.2
Abstract: 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), O n+1(C), SO(p, q + 1), SO n+1(C), and let G' be re-spectively the subgroup GL n(R), GL n(C), U(p, q), O(p, q), O n(C), SO(p, q), SO n(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)⋉H 2n+1(R), GL n(C)⋉ H 2n+1(C), U(p, q)⋉H 2p+2q+1(R), Sp 2n(R)⋉H 2n+1(R), Sp 2n(C)⋉H 2n+1(C), with their respective subgroups GL n(R), GL n(C), U(p, q), Sp 2n(R), and Sp 2n(C).
Source Title: Annals of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103588
ISSN: 0003486X
DOI: 10.4007/annals.2012.175.1.2
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