On Local Descent to Metaplectic Groups and Local Theta Correspondence.

Let F be a p-adic field of characteristic 0. We study a twisted local descent construction for the metaplectic groups Sp ~ 2 n (F) , and also its relation to the corresponding local descent construction for odd special orthogonal groups via local theta correspondence. In consequence, we show that this descent construction gives irreducible supercuspidal genuine representations of Sp ~ 2 n (F) parametrized by a simple local L-parameter φτ corresponding to an irreducible supercuspidal representation τ of GL2n(F) of symplectic type, and the genericity of the representations constructed can be indicated by a local epsilon factor condition. In particular, this local descent construction recovers the local Shimura correspondence for supercuspidal representations. [ABSTRACT FROM AUTHOR]