The Whittaker period formula on Metaplectic SL(2)

Abstract

The Whittaker period formula on metaplectic $SL(2)$ was previously established only when the base field $F$ is totally real. We present a new simple proof that works for all base number fields. Our local argument is uniform at every local place of $F$, based on the isometry property of quadratic Fourier transform and the estimates of matrix coefficients and Whittaker functions imposed by the unitariness of the local representations.

The revised version to appear in Transactions of AMS, 33 pages

References in corpus (3)

• Une formule intégrale reliée à la conjecture locale de Gross-Prasad, 2ème partie: extension aux représentations tempérées
• Model transition for representations of metaplectic type
• On an analogue of the Ichino--Ikeda conjecture for Whittaker coefficients on the metaplectic group

Cited by in corpus (3)

• A conjecture on Whittaker-Fourier coefficients of cusp forms
• Applications of analytic newvectors for $\mathrm{GL}(n)$
• The Bessel Period Functional on SO(5): The Nontempered Case