Invariant Representations of mathrm{GSp}(2) under Tensor Product with a Quadratic Character.

Intro -- Contents -- Abstract -- Chapter 1. Introduction -- 1.1. An Overview -- 1.2. -Invariant Automorphic Representations -- 1.3. Local Character Identities -- 1.4. Statement of Main Results -- 1.5. Acknowledgments -- Chapter 2. -Endoscopy for GSp(2) -- 2.1. Endoscopic Data -- 2.2. Endoscopic group H1 -- 2.3. Endoscopic group H2 -- 2.4. Norm Correspondence -- 2.5. Matching Functions -- Chapter 3. The Trace Formula -- 3.1. The Fine -Expansion -- 3.2. Comparison of the Geometric Sides of Trace Formulas -- 3.3. Application of the Kottwitz-Shelstad Formula -- Chapter 4. Global Lifting -- 4.1. The -Trace Identity -- 4.2. Frobenius-Hecke Classes -- 4.3. Packets -- 4.4. Contributions -- 4.5. Some Global Lifting Results -- 4.6. Final Words -- Chapter 5. The Local Picture -- 5.1. Parabolically Induced Representations -- 5.2. Parabolically Induced Representations---Split Case -- 5.3. Character Identities for Unstable Packets -- 5.4. Character Identities for Stable Packets -- Appendix A. Summary of Global Lifting -- A.1. Unstable (quasi-)packets of G -- A.2. Stable (quasi-)packets -- A.3. Induced representations -- Appendix B. Fundamental Lemma -- B.1. Norm Correspondence---Elliptic Elements -- B.2. Comparison of Orbital Integrals -- Bibliography -- List of Symbols -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.