# The Spectral Side of Stable Local Trace Formula

### Chung Pang Mok

Institute of Mathematics, Academia Sinica, Taipei### Zhifeng Peng

Department of Mathematics, National University of Singapore, Singapore

## Abstract

Let $G$ be a connected quasi-split reductive group over $\mathbb{R}$, and more generally, a quasi-split $K$-group over $\mathbb{R}$. Arthur had obtained the formal formula for the spectral side of the stable local trace formula, by using formal substitute of Langlands parameters. In this paper, we construct the spectral side of the stable local trace formula and endoscopic local trace formula directly for quasi-split $K$-groups over $\mathbb{R}$, by incorporating the works of Shelstad. In particular we give the explicit expression for the spectral side of the stable local trace formula, in terms of Langlands parameters.

## Cite this article

Chung Pang Mok, Zhifeng Peng, The Spectral Side of Stable Local Trace Formula. Doc. Math. 24 (2019), pp. 303–329

DOI 10.4171/DM/682