The distinction problem for metaplectic case.

We use the theta lifts between Mp 2 and P D × to study the distinction problems for the pair ( Mp 2 (E) , SL 2 (F)) , where E is a quadratic field extension over a nonarchimedean local field F of characteristic zero and D is a quaternion algebra. With a similar strategy, we give a conjectural formula for the multiplicity of distinction problem related to the pair ( Mp 2 n (E) , Sp 2 n (F)). [ABSTRACT FROM AUTHOR]