Chapter 1. Introduction ......................................... 1
1.1. An Overview ................................................ 1
1.2. ε-Invariant Automorphic Representations .................... 3
1.3. Local Character Identities ................................. 6
1.4. Statement of Main Results .................................. 7
1.5. Acknowledgments ........................................... 13
Chapter 2. ε-Endoscopy for GSp(2) .............................. 15
2.1. Endoscopic Data ........................................... 15
2.2. Endoscopic group H1 ....................................... 17
2.3. Endoscopic group H2 ....................................... 19
2.4. Norm Correspondence ....................................... 22
2.5. Matching Functions ........................................ 26
Chapter 3. The Trace Formula ................................... 29
3.1. The Fine χ-Expansion ...................................... 29
3.2. Comparison of the Geometric Sides of Trace Formulas ....... 40
3.3. Application of the Kottwitz-Shelstad Formula .............. 44
Chapter 4. Global Lifting ...................................... 47
4.1. The ε-Trace Identity ...................................... 47
4.2. Frobenius-Hecke Classes ................................... 54
4.3. Packets ................................................... 59
4.4. Contributions ............................................. 70
4.5. Some Global Lifting Results ............................... 76
4.6. Final Words ............................................... 82
Chapter 5. The Local Picture ................................... 85
5.1. Parabolically Induced Representations ..................... 87
5.2. Parabolically Induced Representations—Split Case .......... 96
5.3. Character Identities for Unstable Packets ................ 108
5.4. Character Identities for Stable Packets .................. 121
Appendix A. Summary of Global Lifting ......................... 131
A.l. Unstable (quasi-)packets of G ............................ 131
A.2. Stable (quasi-)packets ................................... 131
A.3. Induced representations .................................. 132
Appendix B. Fundamental Lemma ................................. 135
B.l. Norm Correspondence—Elliptic Elements .................... 137
B.2. Comparison of Orbital Integrals .......................... 141
Bibliography .................................................. 163
List of Symbols ............................................... 167
Index ......................................................... 171
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