Endoscopic classification of representations of quasi-split unitary groups

Endoscopic classification of representations of quasi-split unitary groups / Chung Pang Mok.

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Bibliographic Details
Main Author: Mok, Chung Pang, 1981- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2014.
Series:Memoirs of the American Mathematical Society ; Volume 235, no. 1108 (third of 5 numbers)
Subjects:
Linear algebraic groups.
Class field theory.
Algebraic number theory.
Algebraic number theory
Class field theory
Linear algebraic groups
Online Access:Click for online access
Table of Contents:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • Acknowledgement
  • Notation
  • Chapter 2. Statement of the main theorems
  • 2.1.-groups and -embeddings
  • 2.2. Formalism of local parameters
  • 2.3. Formal global parameters
  • 2.4. Endoscopic data and parameters
  • 2.5. Statement of main results
  • 2.6. Review of earlier results
  • Chapter 3. Local character identities and the intertwining relation
  • 3.1. Local endoscopic transfer of test functions
  • 3.2. Characterization of the local classification
  • 3.3. Normalization of local intertwining operators3.4. The local intertwining relation, part I
  • 3.5. The local intertwining relation, part II
  • Chapter 4. Trace formulas and their stabilization
  • 4.1. Discrete part of trace formula
  • 4.2. Stabilization of trace formula
  • 4.3. Preliminary comparison
  • Chapter 5. The Standard model
  • 5.1. Stable multiplicity formula
  • 5.2. The global intertwining relation, part I
  • 5.3. The global intertwining relation, part II
  • 5.4. The spectral expansion, part I
  • 5.5. The spectral expansion, part II
  • 5.6. The endoscopic expansion5.7. The comparison
  • 5.8. The two sign lemmas
  • Chapter 6. Study of Critical Cases
  • 6.1. The case of square-integrable parameters
  • 6.2. The case of elliptic parameters
  • 6.3. Supplementary parameter
  • 6.4. Generic parameters with local constraints
  • Chapter 7. Local Classification
  • 7.1. Resumé on local parameters and local packets
  • 7.2. Construction of global representation
  • 7.3. Construction of global parameter
  • 7.4. The local intertwining relation
  • 7.5. Elliptic orthogonality relation
  • 7.6. Local packets for non square-integrable parameters7.7. Local packets for square-integrable composite parameters
  • 7.8. Local packets for simple parameters
  • 7.9. Resolution
  • Chapter 8. Nontempered representations
  • 8.1. Duality operator of Aubert-Schneider-Stuhler
  • 8.2. Local parameters
  • 8.3. Construction of global parameters with local constraints
  • 8.4. Local packets for square-integrable parameters
  • 8.5. The local intertwining relation
  • Chapter 9. Global classification
  • 9.1. Completion of induction arguments, part I
  • 9.2. Completion of induction arguments, part II9.3. Appendix
  • Chapter 10. Addendum
  • Bibliography
  • Back Cover

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