Towards a generalized Shimura correspondence

DOI10.1016/S0001-8708(86)80010-XzbMath0616.10023OpenAlexW2062110131MaRDI QIDQ1821142

D. A. Kazhdan, Samuel James Patterson

Publication date: 1986

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0001-8708(86)80010-x

zbMATH Keywords

trace formulaprincipal series representationslocal fieldShimura correspondenceWhittaker modelsmetaplectic coverscomparison of charactersgeneralized Shimura correspondencelocal correspondence

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items

On Shimura's correspondence, On the metaplectic analog of Kazhdan's ``endoscopic lifting, On the nonvanishing of some \(L\)-functions, Kazhdan-Patterson lifting for \(GL(n,\mathbb{R})\), Correspondence on characters of irreducible unitary representations of \(GL(n,\mathbb{C})\), Unnamed Item, Local metaplectic correspondence and applications, Dualizing involutions on the metaplectic \(\operatorname{GL}(2)\), Some genuine small representations of a nonlinear double cover, Lifting of characters for nonlinear simply laced groups, Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series, Unnamed Item, Explicit realization of a higher metaplectic representation, Metaplectic correspondence, Unnamed Item, Waldspurger’s involution and lifting of characters, DUALIZING INVOLUTIONS ON THE METAPLECTIC GL(2) à la TUPAN, Explicit realization of a metaplectic representation

Cites Work

• Metaplectic forms
• Automorphic forms on covering groups of GL(2)
• Unstable orbital integrals on SL(3)
• Characters and Jacquet modules
• Regular elements of semisimple algebraic groups
• Automorphic forms on GL (2)
• Higher algebraic K-theory: I
• Introduction to Algebraic K-Theory. (AM-72)
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