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

2013/04/10 by Birgit Speh, Speh, Birgit, Genkai Zhang +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1304.2868

openalex publication_date 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the spherical complementary series of rank one Lie groups H_n=\SO₀(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=\SO₀(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)× 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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• Branching laws for Stein's complementary series and Speh representations of GL(2n,ℝ)

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