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La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique locale

Wen-Wei Li

Abstract

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its preparations, (2) the normalization of intertwining operators subject to Arthur's conditions, (3) the local behavior of characters of admissible representations in the nonarchimedean case, and (4) the genuine part of the invariant local trace formula. As a byproduct of the invariant local trace formula, we deduce the density of tempered characters for coverings.

La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique locale

Abstract

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its preparations, (2) the normalization of intertwining operators subject to Arthur's conditions, (3) the local behavior of characters of admissible representations in the nonarchimedean case, and (4) the genuine part of the invariant local trace formula. As a byproduct of the invariant local trace formula, we deduce the density of tempered characters for coverings.

Paper Structure

This paper contains 44 sections, 26 theorems, 285 equations.

Table of Contents

  1. Introduction
  2. Organisation de cet article
  3. Notations générales
  4. Remerciements
  5. La formule de Plancherel
  6. Définitions de base
  7. Représentations
  8. Fonctions de Schwartz-Harish-Chandra
  9. Opérateurs d'entrelacement
  10. Coefficients d'induites et la fonction c
  11. Énoncé de la formule de Plancherel
  12. Normalisation des opérateurs d'entrelacement
  13. Facteurs normalisants
  14. Le cas archimédien
  15. Le cas non archimédien
  16. ...and 29 more sections

Key Result

Proposition 2.1.1

iFT2]$A_M(F)^\dagger$ Soient $F$ un corps local, $\mathbf{p}: \tilde{G} \to G(F)$ un revêtement à $m$ feuillets. Il existe une famille de sous-groupes $A_M(F)^\dagger$ de $A_M(F)$, où $M$ parcourt les sous-groupes de Lévi de $G$, telle que

Theorems & Definitions (70)

  • Proposition 2.1.1
  • proof
  • Proposition 2.1.2
  • proof
  • Proposition 2.2.1
  • proof
  • Proposition 2.3.1: Cf. Wa03
  • Proposition 2.3.2
  • Proposition 2.4.2
  • Proposition 2.4.3: Cf. Wa03
  • ...and 60 more