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

Abstract

In previous papers we formulated an analogue of the Ichino--Ikeda conjectures for Whittaker--Fourier coefficients of automorphic forms on classical group and the metaplectic group. In the latter case we reduced the conjecture to a local identity. In this paper we will prove the local identity in the $p$-adic case, and hence the global conjecture under simplifying conditions at the archimedean places.

stylistic changes since last version to appear in Algebra and Number Theory

References in corpus (4)

• A conjecture on Whittaker-Fourier coefficients of cusp forms
• Model transition for representations of metaplectic type
• On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups
• Whittaker-Fourier coefficients of cusp forms on ${\widetilde{Sp}}_n$: reduction to a local statement

Cited by in corpus (8)

• Model transition for representations of metaplectic type
• Eisenstein series and the cubic moment for PGL(2)
• Vanishing of certain equivariant distributions on p-adic spherical spaces, and non-vanishing of spherical Bessel functions
• On Whittaker--Fourier coefficients of automorphic forms on unitary groups: reduction to a local identity
• On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\mathrm{GSp}}_4$
• The Whittaker period formula on Metaplectic SL(2)
• On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields
• On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case