| Description |
1 online resource (102 pages) |
| Series |
Memoirs of the American Mathematical Society Ser. ; v. 261 |
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Memoirs of the American Mathematical Society Ser
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| Contents |
880-01 Cover -- Title page -- Chapter 1. Introduction and Main Result -- 1.1. The Ginzburg-Rallis model -- 1.2. Main results -- 1.3. Organization of the paper and remarks on the proofs -- 1.4. Acknowledgements -- Chapter 2. Preliminaries -- 2.1. Notation and conventions -- 2.2. Measures -- 2.3. (,)-families -- 2.4. Weighted orbital integrals -- 2.5. Shalika Germs -- Chapter 3. Quasi-Characters -- 3.1. Neighborhoods of Semisimple Elements -- 3.2. Quasi-characters of () -- 3.3. Quasi-characters of \Fg() -- 3.4. Localization -- Chapter 4. Strongly Cuspidal Functions |
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880-01/(S 4.1. Definition and basic properties -- 4.2. The Lie algebra case -- 4.3. Localization -- Chapter 5. Statement of the Trace Formula -- 5.1. The ingredients of the integral formula -- 5.2. The Main Theorem -- 5.3. The Lie Algebra Case -- Chapter 6. Proof of Theorem 1.3 -- 6.1. Definition of multiplicity -- 6.2. Proof of Theorem 1.3 -- Chapter 7. Localization -- 7.1. A Trivial Case -- 7.2. Localization of _{ }() -- 7.3. Localization of () -- Chapter 8. Integral Transfer -- 8.1. The Problem -- 8.2. Premier Transform -- 8.3. Description of affine space Ξ+Σ -- 8.4. Orbit in Ξ+Λ(B |
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8.5. Local Sections -- 8.6. Calculation of _{ }() -- Chapter 9. Calculation of the limit lim_{ ₂!} _{, }() -- 9.1. Convergence of a premier expression -- 9.2. Combinatorial Definition -- 9.3. Change the truncated function -- 9.4. Proof of 9.3(5) -- 9.5. Proof of 9.3(6) -- 9.6. The split case -- 9.7. Principal proposition -- Chapter 10. Proof of Theorem 5.4 and Theorem 5.7 -- 10.1. Calculation of lim_{ ₂!} _{ }(): the Lie algebra case -- 10.2. A Premier Result -- 10.3. Proof of Theorem 5.4 and Theorem 5.7 -- 10.4. The proof of (_{ }")= (_{ }") |
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Appendix A. The Proof of Lemma 9.1 and Lemma 9.11 -- A.1. The Proof of Lemma 9.1 -- A.2. The proof of Lemma 9.11 -- A.3. A final remark -- Appendix B. The Reduced Model -- B.1. The general setup -- B.2. The trilinear model -- B.3. The generalized trilinear \GL₂ models -- B.4. The middle model -- B.5. The type II models -- Bibliography -- Back Cover |
| Summary |
Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case |
| Notes |
Print version record |
| Subject |
Trace formulas.
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Trace formulas
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| Form |
Electronic book
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| ISBN |
9781470454180 |
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1470454181 |
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