Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups

被引：0
作者：
B. Speh
G. Zhang
机构：
[1] Cornell University,Department of Mathematics
[2] Chalmers University of Technology,Department of Mathematical Sciences
[3] Göteborg University,Department of Mathematical Sciences
来源：
Mathematische Zeitschrift | 2016年 / 283卷
关键词：
Holomorphic Discrete Series; Complementary Series Representations; Discrete Components; Intertwining Operator; Harish-Chandra Modules;
D O I：
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中图分类号：
学科分类号：
摘要：
We consider the spherical complementary series of rank one Lie groups Hn=SO0(n,1;F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_n={ SO }_0(n, 1; {\mathbb {F}})$$\end{document} for F=R,C,H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}$$\end{document}. We prove that there exist finitely many discrete components in its restriction under the subgroup Hn-1=SO0(n-1,1;F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{n-1}={ SO }_0(n-1, 1; {\mathbb {F}})$$\end{document}. This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of Gn=SU(n,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_n=SU(n, 1)$$\end{document}, SU(n,1)×SU(n,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SU(n, 1)\times SU(n, 1)$$\end{document} and SU(2n, 2) and by the branching of holomorphic representations under the corresponding subgroup Gn-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{n-1}$$\end{document}.
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页码：629 / 647
页数：18
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