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

Lapid, Erez; Mao, Zhengyu

doi:10.2140/ant.2017.11.713

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

Erez Lapid and Zhengyu Mao

Vol. 11 (2017), No. 3, 713–765

DOI: 10.2140/ant.2017.11.713

Abstract

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

Keywords

Whittaker coefficients, metaplectic group, automorphic forms

Mathematical Subject Classification 2010

Primary: 11F30

Secondary: 11F70

Milestones

Received: 7 August 2016

Accepted: 16 December 2016

Published: 6 May 2017

Authors

Erez Lapid
Department of Mathematics Weizmann Institute of Science 7610001 Rehovot Israel

Zhengyu Mao
Department of Mathematics and Computer Science Rutgers University Newark, NJ 07102 United States

Vol. 11, No. 3, 2017