The Gross-Prasad conjecture and local theta correspondence

DOI10.1007/s00222-016-0662-8zbMath1358.11061OpenAlexW2962966899WikidataQ122962396 ScholiaQ122962396MaRDI QIDQ2520610

Atsushi Ichino, Gan, Wee Teck

Publication date: 16 December 2016

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-016-0662-8

zbMATH Keywords

unitary groupsGross-Prasad conjectureFourier-Jacobi case

Mathematics Subject Classification ID

Analysis on (p)-adic Lie groups (22E35) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (43)

Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case) ⋮ The local Gan-Gross-Prasad conjecture for \(U(3)\times U(2)\): the non-generic case ⋮ The Shimura-Waldspurger correspondence for \(\mathrm{Mp}_{2n}\) ⋮ Fourier-Jacobi periods and the central value of Rankin-Selberg \(L\)-functions ⋮ On the irreducibility of global descents for even unitary groups and its applications ⋮ Descents of unipotent cuspidal representations of finite classical groups ⋮ On the Gan-Gross-Prasad problem for finite unitary groups ⋮ Local theta lift for \(p\)-adic unitary dual pairs \(\text{U}(2)\times \text{U}(1)\) and \(\text{U}(2)\times \text{U}(3)\) ⋮ Local theta correspondence of tempered representations and Langlands parameters ⋮ On the local Langlands correspondence and Arthur conjecture for even orthogonal groups ⋮ Bessel models for real unitary groups: the tempered case ⋮ Theta lifts and distinction for regular supercuspidal representations ⋮ Spherical varieties, functoriality, and quantization ⋮ Relative trace formulae and the Gan-Gross-Prasad conjectures ⋮ Theta lifting and Langlands functoriality ⋮ On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4 ⋮ Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups ⋮ Twisted GGP problems and conjectures ⋮ Descents of unipotent representations of finite unitary groups ⋮ On gamma factors for representations of finite general linear groups ⋮ A \(p\)-adic arithmetic inner product formula ⋮ Local intertwining relation for metaplectic groups ⋮ Arithmetic theta lifts and the arithmetic Gan-Gross-Prasad conjecture for unitary groups ⋮ Local Langlands correspondence for even orthogonal groups via theta lifts ⋮ Local Langlands correspondence for unitary groups via theta lifts ⋮ The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case ⋮ COMPARISON OF LOCAL RELATIVE CHARACTERS AND THE ICHINO–IKEDA CONJECTURE FOR UNITARY GROUPS ⋮ The Gan-Gross-Prasad conjecture for \(\mathrm{U}(n) \times \mathrm{U}(n)\) ⋮ A local trace formula for the generalized Shalika model ⋮ The Schwartz space of a smooth semi-algebraic stack ⋮ On the residue method for period integrals ⋮ Jacquet modules and local Langlands correspondence ⋮ Theta correspondence for \(p\)-adic dual pairs of type I ⋮ On the non-vanishing of theta liftings of tempered representations of \(U(p,q)\) ⋮ On the Gan-Gross-Prasad problem for finite classical groups ⋮ Chow groups andL-derivatives of automorphic motives for unitary groups, II. ⋮ Chow groups and \(L\)-derivatives of automorphic motives for unitary groups ⋮ A theory of Miyawaki liftings: the Hilbert-Siegel case ⋮ The local Gan-Gross-Prasad conjecture for \(U(n + 1) \times U(n)\): a non-generic case ⋮ Theta lifting for tempered representations of real unitary groups ⋮ Algebraicity of critical values of adjoint \(L\)-functions for \(\mathrm{GSp}_4\) ⋮ Formal degrees and the local theta correspondence: The quaternionic case ⋮ On an algorithm to compute derivatives

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