Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Higher Ext-groups and Relatively Supercuspidal Spectra

Li Cai, Yangyu Fan

Abstract

Relatively supercuspidal representations are analogue of supercuspidal representations in the relative Langlands program. This work studies relatively supercuspidal representations using top degree Ext-groups via the Schneider-Stuhler duality. As examples, the relatively supercuspidal spectra for the Galois case and the triple product case are determined.

Higher Ext-groups and Relatively Supercuspidal Spectra

Abstract

Relatively supercuspidal representations are analogue of supercuspidal representations in the relative Langlands program. This work studies relatively supercuspidal representations using top degree Ext-groups via the Schneider-Stuhler duality. As examples, the relatively supercuspidal spectra for the Galois case and the triple product case are determined.

Paper Structure

This paper contains 9 sections, 27 theorems, 83 equations.

Table of Contents

  1. Introduction
  2. The Flicker-Rallis case
  3. The diagonal case
  4. Notations
  5. Preliminaries
  6. Aubert-Zelevinsky involution and Schneider-Stuhler duality
  7. Relatively supercuspidal representation
  8. The Flicker-Rallis case
  9. The diagonal case

Key Result

Lemma 1.1

Assume $Z_G \cap H = Z_H$. For any irreducible $\pi \in {\mathrm{Rep}}(Z_H(F)\backslash G(F))$ with $\dim{\mathrm{Hom}}_{H(F)}(\pi,{\mathbb {C}})<\infty$, Moreover, $\pi$ is RSC if and only if Here,

Theorems & Definitions (50)

  • Lemma 1.1: See Proposition \ref{['tprsc']} for the general case
  • proof
  • Theorem 1.2
  • Corollary 1.3
  • proof
  • Remark 1.4
  • Remark 1.5
  • Theorem 1.6
  • Theorem 1.7: See Theorem \ref{['diagonal2']}
  • Theorem 1.8: Theorem \ref{['GGP2']}
  • ...and 40 more