In this paper, we verify Vogan＇s conjecture on quantization in the representation theory for G = GL（n, C）. Also we get some relationship between the induction of orbits and Howe＇s θ-lifting of unitary representat...In this paper, we verify Vogan＇s conjecture on quantization in the representation theory for G = GL（n, C）. Also we get some relationship between the induction of orbits and Howe＇s θ-lifting of unitary representations展开更多
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
We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the me...We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the meaning of Vogan’s conjecture.Therefore,when verifying Vogan’s conjecture,many cases can be reduced to the case of rigid orbit data.展开更多
基金The author would like to thank Professor Jing-Song Huang and Professor Fu-Hai Zhu for very helpful suggestion. This work was supported in part by the National Natural Science Foundation of China （Grant No. 10971103）.
文摘In this paper, we verify Vogan＇s conjecture on quantization in the representation theory for G = GL（n, C）. Also we get some relationship between the induction of orbits and Howe＇s θ-lifting of unitary representations
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.
基金supported by National Natural Science Foundation of China(Grant No.10971103)
文摘We use induced orbit covers to define induced orbit data.By studying the space of regular functions on orbit cover,we know that the induced representation has close connection with the induced orbit datum under the meaning of Vogan’s conjecture.Therefore,when verifying Vogan’s conjecture,many cases can be reduced to the case of rigid orbit data.
