Uniqueness and existence of Whittaker models for the metaplectic group

DOI10.1007/BF02761822zbMath0441.22015OpenAlexW2031320921WikidataQ101488900 ScholiaQ101488900MaRDI QIDQ1142876

Ilya I. Piatetski-Shapiro, Stephen Gelbart, Roger E. Howe

Publication date: 1979

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02761822

zbMATH Keywords

automorphic formsL-functionsWhittaker modelsGL2metaplectic covering groupspherical function algebra

Mathematics Subject Classification ID

(p)-adic theory, local fields (11F85) Representations of Lie and linear algebraic groups over local fields (22E50) Harmonic analysis and spherical functions (43A90)

Related Items (14)

Restriction of representations of metaplectic \(\mathrm{GL}_{2}(F)\) to tori ⋮ Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger ⋮ Branching laws for the metaplectic cover of \(\operatorname{GL}_2\) ⋮ Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method ⋮ Distinguished representations and modular forms of half-integral weight ⋮ On Supercuspidal Representations of the Metaplectic Group ⋮ Functional equations and gamma factors of local zeta functions for the metaplectic cover of \(\mathrm{SL}_2\) ⋮ Generalized Bump-Hoffstein conjecture for coverings of the general linear groups ⋮ Some results in the theory of genuine representations of the metaplectic double cover of \(GSp_{2n}(F)\) over \(p\)-adic fields ⋮ Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series ⋮ Uniqueness of Whittaker functionals on the metaplectic group ⋮ Waldspurger’s involution and lifting of characters ⋮ Modular forms ⋮ Metaplectic forms

Cites Work

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• Distinguished representations and modular forms of half-integral weight
• Weil's representation and the spectrum of the metaplectic group
• Automorphic forms on GL (2)
• Automorphic L -functions of half-integral weight

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