The Super-cuspidal Representation Of Sp₄（k）

Bruhat-Tits Building,named after F.Bruhat and J.Tits, has been used to study the structure of the homogeneous spaces of p-adic Lie groups. Moy and Prasad have found an application of the building theory. They have defined the depth of an irreducible admissible complex representation of G and classified all depth-zero irreducible super-cuspidal representation.The thesis contains three parts:In chapter 1,1 will introduce the Bruhat-Tits building theory and present a question that classifying all the super-cuspidal representation of G which fixes the point v. In chapter 2, I will introduce the representation of SL2(Fq) via Deligne-Lusztig theory. In chapter 3,1 will classifying all the super-cuspidal representation of G which fixes the point v based on the method of Moy and Prasad.