Twisted endoscopy from a sheaf-theoretic perspective

TL;DR

This paper extends the sheaf-theoretic approach to twisted endoscopy, enabling new applications in computing Arthur packets for real groups, bridging harmonic analysis and sheaf theory.

Contribution

It introduces a sheaf-theoretic framework for twisted endoscopy, expanding the existing theory and facilitating computations of Arthur packets.

Findings

Extended sheaf-theoretic formulation to twisted endoscopy.

Provided methods for computing Arthur packets.

Bridged harmonic analysis and sheaf theory approaches.

Abstract

The standard theory of endoscopy for real groups has two parallel formulations. The original formulation of Langlands and Shelstad relies on methods in harmonic analysis. The subsequent formulation of Adams, Barbasch and Vogan relies on sheaf-theoretic methods. The original formulation was extended by Kottwitz and Shelstad to twisted endoscopy. We extend the sheaf-theoretic formulation to the context of twisted endoscopy and provide applications for computing Arthur packets.