2019/07/14 by Toshiyuki Kobayashi, Kobayashi, Toshiyuki, Birgit Speh +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1907.05890
openalex publication_date 2019/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given irreducible representations Π and π of the rank one special orthogonal groups G=SO(n+1,1) and G'=SO(n,1) with nonsingular integral infinitesimal character, we state in terms of θ-stable parameter necessary and sufficient conditions so that HomG'(Π|G', π)\not = \0\. In the special case that both Π and π are tempered, this implies the Gross--Prasad conjectures for tempered representations of SO(n+1,1) × SO(n,1) which are nontrivial on the center. We apply these results to construct nonzero periods and distinguished representations. If both Π and π have the trivial infinitesimal character ρ then we use a theorem that the periods are nonzero on the minimal K-type to obtain a nontrivial bilinear form on the (\mathfrak g,K)-cohomology of the representations.