Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups |
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Authors: | Email author" target="_blank">B?SpehEmail author G?Zhang |
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Institution: | 1.Department of Mathematics,Cornell University,Ithaca,USA;2.Department of Mathematical Sciences,Chalmers University of Technology,G?teborg,Sweden;3.Department of Mathematical Sciences,G?teborg University,G?teborg,Sweden |
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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(2n, 2) and by the branching of holomorphic representations under the corresponding subgroup \(G_{n-1}\). |
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