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Theta lifting and Langlands functoriality - MaRDI portal

Theta lifting and Langlands functoriality (Q6119687)

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scientific article; zbMATH DE number 7823045

Language	Label	Description	Also known as
English	Theta lifting and Langlands functoriality	scientific article; zbMATH DE number 7823045

Statements

scholarly article

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Theta lifting and Langlands functoriality (English)

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International Congress of Mathematicians

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publication date

24 March 2024

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Summary: We review various aspects of theta lifting and its role in studying Langlands functoriality. In particular, we discuss realizations of the Jacquet-Langlands correspondence and the Shimura-Waldspurger correspondence in terms of theta lifting and their arithmetic applications. For the entire collection see [Zbl 07816357].

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zbMATH Keywords

automorphic representations

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Langlands functoriality

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theta lifting

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.4171/icm2022/82

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The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case

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Local theta correspondence of tempered representations and Langlands parameters

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Theta correspondence for \(p\)-adic dual pairs of type I

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Expression d'un facteur epsilon de paire par une formule intégrale

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Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires

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La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes unitaires

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Plancherel formula for \(\mathrm{GL}_n(F)\setminus \mathrm{GL}_n(E)\) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups

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COMPARISON OF LOCAL RELATIVE CHARACTERS AND THE ICHINO–IKEDA CONJECTURE FOR UNITARY GROUPS

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Isolation of cuspidal spectrum, with application to the Gan-Gross-Prasad conjecture

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On lifting from classical groups to \(\text{GL}_N\)

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Functoriality for the classical groups

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Quadratische Formen und Modulfunktionen

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Finiteness theorems for abelian varieties over number fields.

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Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

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Formal degrees and local theta correspondence

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The Gross-Prasad conjecture and local theta correspondence

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The Shimura-Waldspurger correspondence for \(\mathrm{Mp}_{2n}\)

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The Automorphic Discrete Spectrum of Mp4

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Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence

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A proof of the Howe duality conjecture

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On the Decomposition of a Representation of SO<sub>n</sub> When Restricted to SO<sub>n-1</sub>

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On Irreducible Representations of So<sub>2n+1</sub> × So<sub>2m</sub>

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The central critical value of a triple product \(L\)-function

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Formal degrees and adjoint 𝛾-factors

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Transcending Classical Invariant Theory

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Trilinear forms and the central values of triple product \(L\)-functions

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On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture

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On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

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Periods of Quaternionic Shimura Varieties. I.

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Automorphic forms on GL (2)

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The theta correspondence and harmonic forms. I

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Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables

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Problems in the theory of automorphic forms to Salomon Bochner in gratitude

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On an analogue of the Ichino-Ikeda conjecture for Whittaker coefficients on the metaplectic group

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Automorphic forms with degenerate Fourier coefficients

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La conjecture locale de Gross-Prasad pour les groupes sp\'eciaux orthogonaux: le cas g\'en\'eral

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Modular forms of half integral weight and the integral of certain theta-functions

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On zeta functions of quaternion algebras

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Theta series and automorphic forms on \(\text{GL}_2\)

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On modular forms of half integral weight

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On construction of holomorphic cusp forms of half integral weight

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Shimura and Shintani correspondences

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Correspondances de Shimura et quaternions

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Une formule intégrale reliée à la conjecture locale de Gross–Prasad

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La conjecture locale de Gross-Prasad pour les repr\'esentations temp\'er\'ees des groupes sp\'eciaux orthogonaux

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Sur certains groupes d'opérateurs unitaires

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On the global Gan-Gross-Prasad conjecture for unitary groups: approximating smooth transfer of Jacquet-Rallis

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Automorphic period and the central value of Rankin-Selberg L-function

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Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups

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Identifiers

10.4171/icm2022/82

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6119687

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