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- Title
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups.
- Authors
Speh, B.; Zhang, G.
- Abstract
We consider the spherical complementary series of rank one Lie groups $$H_n={ SO }_0(n, 1; {\mathbb {F}})$$ for $${\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}$$ . We prove that there exist finitely many discrete components in its restriction under the subgroup $$H_{n-1}={ SO }_0(n-1, 1; {\mathbb {F}})$$ . This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of $$G_n=SU(n, 1)$$ , $$SU(n, 1)\times SU(n, 1)$$ and SU(2 n, 2) and by the branching of holomorphic representations under the corresponding subgroup $$G_{n-1}$$ .
- Publication
Mathematische Zeitschrift, 2016, Vol 283, Issue 1/2, p629
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-016-1614-0