A Local Relative Trace Formula for the Ginzburg-Rallis Model

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Wan, Chen
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2019.
Colección:Memoirs of the American Mathematical Society Ser.
Temas:
Trace formulas.
Formules de trace.
Trace formulas
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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 (_{ }")= (_{ }")
  • 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

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