Hecke duality of Ikeda lifts

Garrett, Paul; Heim, Bernhard

doi:10.1016/j.jnt.2014.01.030

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2019

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“…Ichino [24] and Xue [50] proved Conjecture 1.3 (1) for the case where r = 1 independently. Garrett-Heim [15] established a Hecke duality of Ikeda liftings and gave a preliminary answer to Conjecture 1.3 (1). Recently, Ikeda-Yamana [28] extended the theory of Ikeda liftings.…”

Section: Introductionmentioning

confidence: 99%

“…Ichino [24] and Xue [50] proved Conjecture 1.3 (1) for the case where r = 1 independently. Garrett-Heim [15] established a Hecke duality of Ikeda liftings and gave a preliminary answer to Conjecture 1.3 (1). Nowadays Miyawaki's conjecture (Conjecture 1.1) follows from Arthur's multiplicity formula ([2, Theorem 1.5.2]), which was established in 2013.…”

Section: Introductionmentioning

confidence: 99%

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A theory of Miyawaki liftings: the Hilbert–Siegel case

Atobe

2019

Math. Ann.

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The Miyawaki liftings are defined by the pullbacks of Ikeda liftings. Recently, Ikeda and Yamana extended the theory of Ikeda liftings. In this paper, using their results, we establish a theory of Miyawaki liftings, both locally and globally. In the local theory, we describe the Miyawaki liftings for almost tempered unitary representations explicitly. In the global theory, we discuss the non-vanishing of the Miyawaki liftings using seesaw identities and the global Gan-Gross-Prasad conjecture. As an application of local Miyawaki liftings, we prove a new case of the local Gan-Gross-Prasad conjecture.

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Section: Introductionmentioning

confidence: 99%

“…Ichino [24] and Xue [50] proved Conjecture 1.3 (1) for the case where r = 1 independently. Garrett-Heim [15] established a Hecke duality of Ikeda liftings and gave a preliminary answer to Conjecture 1.3 (1). Nowadays Miyawaki's conjecture (Conjecture 1.1) follows from Arthur's multiplicity formula ([2, Theorem 1.5.2]), which was established in 2013.…”

Section: Introductionmentioning

confidence: 99%

A theory of Miyawaki liftings: the Hilbert–Siegel case

Atobe

2019

Math. Ann.

View full text Add to dashboard Cite

show abstract

Hecke duality of Ikeda lifts

Cited by 1 publication

References 33 publications

A theory of Miyawaki liftings: the Hilbert–Siegel case

A theory of Miyawaki liftings: the Hilbert–Siegel case

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