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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer Berlin Heidelberg

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DOI

10.1016/0921-4526(91)90142-2

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1432-1823

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Restriction to symmetric subgroups of unitary repr

Authors: B Speh G Zhang
Publish Date: 2016/01/21
Volume: 283, Issue: 1-2, Pages: 629-647
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Abstract

We consider the spherical complementary series of rank one Lie groups H n= SO 0n 1 mathbb F for mathbb F=mathbb R mathbb C mathbb H We prove that there exist finitely many discrete components in its restriction under the subgroup H n1= SO 0n1 1 mathbb F This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of G n=SUn 1 SUn 1times SUn 1 and SU2n 2 and by the branching of holomorphic representations under the corresponding subgroup G n1

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