Cuspidal Representations : Explicit Classification of Cuspidal Representations for GL(2)
- 주제(키워드) Cuspidal Representations
- 발행기관 고려대학교 대학원
- 지도교수 김동균
- 발행년도 2014
- 학위수여년월 2014. 8
- 학위구분 석사
- 학과 일반대학원 수학과
- 원문페이지 41 p
- 실제URI http://www.dcollection.net/handler/korea/000000051788
- 본문언어 한국어
- 제출원본 000045808777
초록/요약
The object of these notes is to classify the irreducible cuspidal representations of G = GL2. We introduce a chain order, a fundamental stratum and then classify fundamental stratum for examples. Moreover, we characterize the cuspidal representations, which we then rene to a classication. I studied the representations with the book, \The local langlands conjecture for GL(2)". It is a very good book, but doesn't have enough explanations and examples. I want other students to read this book more conveniently, so I started this treatise. I preinform that most of contents is from the book, \The local langlands conjecture for GL(2)."
more목차
1. Introduction 1
2. Chain Orders and Fundamental Strata 1
2.1. Lattice Chains 1
2.2. Chain Orders 4
2.3. Examples of Chain Orders 7
2.4. Applications of Chain Orders 8
2.5. Duality 11
2.6. Normalized Level 14
2.7. Strata 14
2.8. Fundamental Strata 15
2.9. Properties of Fundamental Strata 18
3. Classi cation of Fundamental Strata 19
3.1. Rami ed Simple Strata 19
3.2. Other Fundamental Strata 20
3.3. Properties of Essentially Scalar Strata 21
3.4. Relations of Minimal and Simple Strata 1 22
3.5. Relations of Minimal and Simple Strata 2 25
4. Strata and the Principal Series 25
4.1. Properties of Split Fundamental Strata 25
4.2. Fundamental Strata in Induced Representations 27
4.3. The Principal Series 28
4.4. Exhaution Theorem 29
5. Classi cation of Cuspidal Representations 30
5.1. Intertwining Theorem 30
5.2. Conjugacy Theorem 32
5.3. Cuspidal Representations 33
5.4. The Uniqueness Property 34
5.5. Cuspidal Types 34
5.6. Structures of Cuspidal Types 35
5.7. Useful Consequences 37
5.8. Cuspidal Inducing Data 37
References 39
