Discrete Components of Some Complementary Series

2009/02/26 by T. N. Venkataramana, Venkataramana, T. N., Birgit Speh +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0902.4620

arxiv created 2009/02/26 · openalex publication_date 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that complementary series representations of SO(n,1) contain discretely complementary series of SO(m,1) provided the continuous parameter is sufficiently close to the first point of reducibility and the representation of the compact part of the Levi is a sufficiently small fundamental representation. We prove as a consequence that cohomological representations of SO(n,1) of degree i less than m/2 contain discretely, cohomogical representations of SO(m,1).

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