Refined global Gan-Gross-Prasad conjecture for Fourier-Jacobi periods on symplectic groups

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4 Scopus citations

Abstract

In this paper, we propose a conjectural identity between the Fourier-Jacobi periods on symplectic groups and the central value of certain Rankin-Selberg -functions. This identity can be viewed as a refinement to the global Gan-Gross-Prasad conjecture for . To support this conjectural identity, we show that when and , it can be deduced from the Ichino-Ikeda conjecture in some cases via theta correspondences. As a corollary, the conjectural identity holds when or when , and the automorphic representation on the bigger group is endoscopic.

Original languageEnglish (US)
Pages (from-to)68-131
Number of pages64
JournalCompositio Mathematica
Volume153
Issue number1
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

Keywords

  • Fourier-Jacobi periods
  • Gan-Gross-Prasad conjectures

ASJC Scopus subject areas

  • Algebra and Number Theory

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