Tensor products of complementary series of rank one Lie groups

2014/02/12 by Genkai Zhang, Zhang, Genkai
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1402.2950

openalex publication_date 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the tensor product π_α⊗ π_β of complementary series representations π_α and π_β of classical rank one groups SO₀(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_α+β for small parameters α, β (in our parametrization). We prove further that for G=SO₀(n, 1) there are finitely many complementary series of the form π_{α+β+ 2j}, j=0, 1, ⋯, k, appearing in the tensor product π_α ⊗ π_β of two complementary series π_α and π_β, where k=k(α, β, n) depends on α, β, n.

Citations

• Differential symmetry breaking operators. I-Genreal theory and F-method. II-Rankin-Cohen Operators for Symmetric Pairs

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