Shalika models of GL(4) over a finite field

• Main Authors: Chih-HsuanTsai, 蔡誌軒
• Other Authors: Chufeng Nien
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/f63tnj

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 106 === The goal of this paper is to determine whether a irreducible representation of GL(4) over a finite field admits a shalika model. We analysis it for two parts:cuspidal representations and noncuspidal representations. For cuspidal representations, we use a result published from mathematician Dipendra Prasad at 2000. From the result, it is easy to determine whether a cuspidal representation has a Shalika model. For noncuspidal representations, by the definition of cuspidal, we see a noncuspidal representation as a subrepresentation of an parabolic induction from some parabolic induction subgroup of GL(4). We consider all parabolic inductions of GL(4) and use a well-known theorem Mackey’s theorem to determined whether a parabolic induction has a Shalika model. From Mackey’s theorem, we get some condition for a parabolic induction has a Shalika model and use it to get some result.