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

Date of Award | 2018 Jul 10 |
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Original language | English |
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Supervisor | Chufeng Nien (Supervisor) |
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Shalika models of GL(4) over a finite field

誌軒, 蔡. (Author). 2018 Jul 10

Student thesis: Master's Thesis