P-the Adic Sp <sub> 4 </ Sub> Supercuspidal Constructed In The Data

By Harish-Chandra Cuspidal Principle(Theorem 1.1),the classfication problem of irreducible admissible representations of general connected reductive p-adic groups is devided into two parts:first,construct all irreducible supercuspidal representations,second,study the induced representations from irreducible supercuspidal representations of parabolic subgroups.Therefore,construction of irreducible supercuspidal representations is very important in the theory of representations of p-adic groups and the theory of automorphic froms and representations.This thesis mainly consider the construction of irreducible supercuspidal representations of simply-connected reductive group G = Sp₄(F), where F is a non-archimedean local field of characteristic 0.In Chapter 1,we briefly introduce the background of this topic,and summarize known results and recent progress on the construction of supercuspidal representations.In Chapter 2,we briefly review the Bruhat-Tits building theory of G.In Chapter 3,we describe the construction of all depth-zero supercnspidai representations of G,based on A.Moy and G.Prasad's general classification theory on depth-zero supercuspidal representations.In chapter 4,we introduce the general method of J.K.Yu on the construction of tame supercuspidal representations.In chapter 5,we consider the computation of some construction data of tame supercnspidai representations of G,using J.K.Yu's method.The residue characteristic of F is considered to be odd in the chapter 5.Chapter 6 is a summary.