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A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side.
About this Title
Chen Wan, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Publication: Memoirs of the American Mathematical Society
Publication Year:
2019; Volume 261, Number 1263
ISBNs: 978-1-4704-3686-5 (print); 978-1-4704-5418-0 (online)
DOI: https://doi.org/10.1090/memo/1263
Published electronically: November 6, 2019
Keywords: Harmonic analysis on spherical variety,
representation of p-adic group,
local trace formula,
multiplicity one on Vogan packet
MSC: Primary 22E35, 22E50
Table of Contents
Chapters
- 1. Introduction and Main Result
- 2. Preliminaries
- 3. Quasi-Characters
- 4. Strongly Cuspidal Functions
- 5. Statement of the Trace Formula
- 6. Proof of Theorem
- 7. Localization
- 8. Integral Transfer
- 9. Calculation of the limit $\lim _{N\rightarrow \infty } I_{x,\omega ,N}(f)$
- 10. Proof of Theorem and Theorem
- A. The Proof of Lemma and Lemma
- B. The Reduced Model
Abstract
Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, we are able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, we prove a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, we prove the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.- James Arthur, The trace formula in invariant form, Ann. of Math. (2) 114 (1981), no. 1, 1–74. MR 625344, DOI 10.2307/1971376
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