Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs

2008/10/16 by Shuichiro Takeda, Takeda, Shuichiro
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.0810.2990

openalex publication_date 2008/10/16 · arxiv created 2010/05/12 · arxiv updated 2010/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Following the approach of B. Roberts, we characterize the non-vanishing of global theta lifts for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's work by a certain weaker assumption, and apply our results to small rank similitude groups. Among our applications is a certain instance of Langlands functorial transfer of a (non-generic) cuspidal automorphic representation of GSp(4) to GL(4).

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