Theta correspondence and the Prasad conjecture for SL(2)

Hengfei Lu

Vol. 295 (2018), No. 2, 477–498

DOI: 10.2140/pjm.2018.295.477

Abstract

We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of $SL\left(2\right)$ over a nonarchimedean quadratic field extension $E∕F$. Then we verify the Prasad conjecture for  $SL\left(2\right)$. With a similar strategy, we obtain a certain result for the Prasad conjecture for $Sp\left(4\right)$.

Keywords

theta lifts, periods, base change, Prasad's conjecture

Mathematical Subject Classification 2010

Primary: 11F27, 11F70, 22E50

Milestones

Received: 12 September 2017

Revised: 6 February 2018

Accepted: 22 February 2018

Published: 11 April 2018