Conservation relations for local theta correspondence

DOI10.1090/S0894-0347-2014-00817-1zbMath1321.22017arXiv1204.2969MaRDI QIDQ5264115

Chen-Bo Zhu, Bin Yong Sun

Publication date: 20 July 2015

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2969

zbMATH Keywords

degenerate principal serieslocal theta correspondenceoscillator representationsconservation relation

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Theta series; Weil representation; theta correspondences (11F27) Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items (45)

The distinction problems for \(\operatorname{Sp}_4\) and \(\operatorname{SO}_{3,3}\) ⋮ The Shimura-Waldspurger correspondence for \(\mathrm{Mp}_{2n}\) ⋮ Local theta correspondences between epipelagic supercuspidal representations ⋮ Local Theta Correspondences between Supercuspidal Representations ⋮ The explicit theta correspondence for reductive dual pairs \((\mathrm{Sp}(p,q),O^{\ast}(4))\) ⋮ Characters of irreducible unitary representations of 𝑈(𝑛,𝑛+1) via double lifting from 𝑈(1) ⋮ On the theta correspondence for (𝐺𝑆𝑝(4),𝐺𝑆𝑂(4,2)) and Shalika periods ⋮ Generic representations of metaplectic groups and their theta lifts ⋮ Explicit induction principle and symplectic-orthogonal theta lifts ⋮ Local theta correspondence of tempered representations and Langlands parameters ⋮ Coincidence of algebraic and smooth theta correspondences ⋮ Hodge classes and the Jacquet–Langlands correspondence ⋮ The Local Langlands Conjecture for ⋮ \(R\)-groups for metaplectic groups ⋮ Theta lifts and distinction for regular supercuspidal representations ⋮ Theta lifts of generic representations: the case of odd orthogonal groups ⋮ Automorphic descent for symplectic groups: The branching problems and L -functions ⋮ On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4 ⋮ PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS ⋮ Howe duality and dichotomy for exceptional theta correspondences ⋮ Generic Hecke algebra and theta correspondence over finite fields ⋮ Automorphic forms, geometry and arithmetic. Abstracts from the workshop held August 22--28, 2021 (hybrid meeting) ⋮ The Prasad conjectures for \(\mathrm{GSp}_4\) and \(\mathrm{PGSp}_4\) ⋮ Formal degrees and local theta correspondence ⋮ The distinction problem for metaplectic case ⋮ The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula ⋮ SUR LES PAQUETS D’ARTHUR DE CONTENANT DES MODULES UNITAIRES DE PLUS HAUT POIDS, SCALAIRES ⋮ Local Langlands correspondence for even orthogonal groups via theta lifts ⋮ Theta correspondence and the Prasad conjecture for \(\operatorname{SL}(2)\) ⋮ Local Langlands correspondence for unitary groups via theta lifts ⋮ \(L\)-functions and theta correspondence for classical groups ⋮ On the cohomology of some complex hyperbolic arithmetic 3-manifolds ⋮ The \(\mathrm{PGSp}_{1,1}(\mathbb{A})\)-distinguished representations ⋮ Mixed Arithmetic Theta Lifting for Unitary Groups ⋮ Theta lifts of generic representations for dual pairs \((\mathrm{Sp}_{2n}, \mathrm{O}(V))\) ⋮ First occurrence indices of tempered representations of metaplectic groups ⋮ Theta correspondence for \(p\)-adic dual pairs of type I ⋮ A note on the local theta correspondence for unitary similitude dual pairs ⋮ On the non-vanishing of theta liftings of tempered representations of \(U(p,q)\) ⋮ The Gross-Prasad conjecture and local theta correspondence ⋮ Symplectic models for unitary groups ⋮ The \(\operatorname{SL}_1(D)\)-distinction problem ⋮ Remarks on the theta correspondence over finite fields ⋮ The non-tempered \(\theta_{10}\) Arthur parameter and Gross-Prasad conjectures ⋮ Formal degrees and the local theta correspondence: The quaternionic case

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