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 ortho...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.展开更多
The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
文摘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.
文摘The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
