摘要
Let F be a p-adic field of characteristic 0.We study a twisted local descent construction for the metaplectic groups Sp2 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 Sp2n(-F)parametrized by a simple local L-parameterφτcorresponding to an irreducible supercuspidal representationτof 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.
基金
Supported by NSFC(Grant No.11501382)。
