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The local twisted Gan-Gross-Prasad conjecture for $\text{U}(V_K)/\text{U}(V)$

Nhat Hoang Le

Abstract

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)/U(V)$ for tempered $L$-parameters over nonarchimedean fields of odd residual characteristic.

The local twisted Gan-Gross-Prasad conjecture for $\text{U}(V_K)/\text{U}(V)$

Abstract

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for for tempered -parameters over nonarchimedean fields of odd residual characteristic.

Paper Structure

This paper contains 65 sections, 52 theorems, 383 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. Geometric formula for $m_V(\pi)$
  4. Geometric expansion of the twisted multiplicity $\varepsilon_\psi(\tilde{\pi})$
  5. Organization of the paper
  6. Preliminaries
  7. Groups, measures and notations
  8. Representations
  9. $(G,M)$-families and $(\tilde{G},\tilde{M})$-families
  10. Harish-Chandra semisimple descent and the descent to Lie algebra
  11. Quasi-characters
  12. Strongly cuspidal functions
  13. Weighted orbital integrals of strongly cuspidal functions
  14. Weighted characters of strongly cuspidal functions
  15. Quasi-characters attached to strongly cuspidal functions
  16. ...and 50 more sections

Key Result

Theorem 1.2

Theorems & Definitions (83)

  • Conjecture 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Proposition 2.1
  • Proposition 2.2
  • Definition 2.3
  • Lemma 2.4
  • Lemma 2.5
  • ...and 73 more