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On Jiang's wavefront sets conjecture for representations in local Arthur packets

Baiying Liu, Freydoon Shahidi

Abstract

This note serves as an attempt towards the Jiang conjecture on the upper bound nilpotent orbits in the wavefront sets of representations in local Arthur packets of classical groups, which is a natural generalization of the well-known Shahidi conjecture, reflecting the relation between the structure of wavefront sets and the local Arthur parameters. Applying the character identities of local Arthur packets and the matching method of endoscopic liftings, we reduce the study of the upper bound to certain properties of the wavefront sets of the corresponding bi-torsor representations of general linear groups.

On Jiang's wavefront sets conjecture for representations in local Arthur packets

Abstract

This note serves as an attempt towards the Jiang conjecture on the upper bound nilpotent orbits in the wavefront sets of representations in local Arthur packets of classical groups, which is a natural generalization of the well-known Shahidi conjecture, reflecting the relation between the structure of wavefront sets and the local Arthur parameters. Applying the character identities of local Arthur packets and the matching method of endoscopic liftings, we reduce the study of the upper bound to certain properties of the wavefront sets of the corresponding bi-torsor representations of general linear groups.
Paper Structure (9 sections, 28 theorems, 230 equations)

This paper contains 9 sections, 28 theorems, 230 equations.

Table of Contents

  1. Introduction
  2. Characterization of local Arthur packets
  3. Twisted Jacquet modules associated to nilpotent orbits
  4. Dimension identities for nilpotent orbits
  5. Character expansions
  6. Dimension identities for nilpotent orbits
  7. Construction of elements in local Arthur packets
  8. Proof of Theorems \ref{['mainintro']} and \ref{['mainintroextra']}
  9. On central characters of representations in local Arthur packets, by Alexander Hazeltine, Baiying Liu, Chi-Heng Lo, and Freydoon Shahidi

Key Result

Theorem 1.1

Theorems & Definitions (51)

  • Theorem 1.1
  • Conjecture 1.2
  • Conjecture 1.3
  • Remark 1.4
  • Conjecture 1.5: Shahidi Conjecture
  • Conjecture 1.6: Enhanced Shahidi Conjecture
  • Conjecture 1.7: Jiang Conjecture
  • Definition 1.8
  • Theorem 1.9
  • Remark 1.10
  • ...and 41 more