Lifting cusp forms on \(\text{GL}_{2n}\) to \(\widetilde{\text{Sp}}_{2n}\): The unramified correspondence

DOI10.1215/S0012-7094-99-10009-3zbMath0991.11024OpenAlexW2043195836MaRDI QIDQ1974963

Stephen Rallis, David Soudry, David Ginzburg

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-10009-3

zbMATH Keywords

liftEisenstein seriestheta function\(L\)-functionFourier-Jacobi coefficientsJacquet modulemetaplectic covermultiplicity one theoremgeneralization of the classical Shimura correspondenceJacobi moduleself-dual cuspidal automorphic representations

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (10)

On the nonvanishing of the central value of the Rankin-Selberg 𝐿-functions ⋮ On correspondences between certain automorphic forms on \(\mathrm{Sp}_{4n} (\mathbb{A})\) and \(\widetilde{\mathrm{Sp}}_{2n} (\mathbb{A})\) ⋮ Periods of automorphic forms, poles of \(L\)-functions and functorial lifting ⋮ Automorphic descent for symplectic groups: The branching problems and L -functions ⋮ A FUNDAMENTAL LEMMA BETWEEN THE SYMPLECTIC AND THE METAPLECTIC GROUP: THE NON-SPLIT CASE ⋮ Descent Construction for GSpin groups ⋮ A conjecture on Whittaker-Fourier coefficients of cusp forms ⋮ Endoscopic lifting in classical groups and poles of tensor \(L\)-functions ⋮ On local descent to metaplectic groups and local theta correspondence ⋮ A Plancherel formula for Sp_2n/Sp_n×Sp_n and its application

Cites Work

• On explicit lifts of cusp forms from \(\text{GL}_m\) to classical groups
• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II
• $L$-functions for symplectic groups
• On a correspondence between cuspidal representations of 𝐺𝐿_{2𝑛} and 𝑆𝑝̃_{2𝑛}
• Unnamed Item

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