2023/07/04 by Chunhui Wang, Wang, Chun-Hui
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2307.01581
openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be the usual real field. Let W be a symplectic vector space over F. It is known that there are two different Weil representations of a Meteplectic covering group \widetildeSp(W). By some twisted actions, we reorganize them into a representation of \widetildeSp±(W), a covering group over a subgroup Sp±(W) of GSp(W). Based on the works of MVW, Kudla, and Howe on reductive dual pairs in Sp(W), we explore the analogous dual pairs in Sp±(W) . Finally, following Lion-Vergne's classical book on Weil representations and theta series, we investigate some simple theta series in Sp±(W) where W has dimension two.