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Construction of Local Arthur Packets for Metaplectic Groups and the Adams Conjecture

Jiahe Chen

Abstract

In this article, we explicitly construct local Arthur packets for metaplectic groups over non-Archimedean local fields of characteristic zero. Our construction is a generalization of Atobe's construction of local Arthur packets for classical groups. As a result, we prove that the local Arthur packets are multiplicity free. Moreover, we generalize Moeglin's earlier work about the Adams conjecture to metaplectic groups.

Construction of Local Arthur Packets for Metaplectic Groups and the Adams Conjecture

Abstract

In this article, we explicitly construct local Arthur packets for metaplectic groups over non-Archimedean local fields of characteristic zero. Our construction is a generalization of Atobe's construction of local Arthur packets for classical groups. As a result, we prove that the local Arthur packets are multiplicity free. Moreover, we generalize Moeglin's earlier work about the Adams conjecture to metaplectic groups.
Paper Structure (49 sections, 83 theorems, 195 equations)

This paper contains 49 sections, 83 theorems, 195 equations.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Generalized segments
  4. Metaplectic groups
  5. Endoscopy
  6. Arthur parameters
  7. Arthur packets
  8. Langlands correspondence
  9. Theta correspondence
  10. Derivatives and socles
  11. Partial Jacquet modules and socles
  12. The non-self-dual case
  13. Self-dual case
  14. Discrete series
  15. Computation of partial Jacquet module
  16. ...and 34 more sections

Key Result

Theorem 1.1

(Theorem theorem: A-packets can be constructed via extended multi-segments) Let $\psi$ be an Arthur parameter of good parity. For $\varepsilon\in\mathcal{S}_\psi^\vee$, we have $\pi_\mathrm{Ato}(\psi,\varepsilon)=\bigoplus\pi(\mathcal{E})$, where $\mathcal{E}$ runs over all equivalence classes of ex

Theorems & Definitions (174)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Conjecture 1.4
  • Theorem 1.5
  • Proposition 2.1
  • Proposition 2.2
  • proof
  • Theorem 2.3
  • Theorem 2.4
  • ...and 164 more