Discrete series L-packets for real reductive groups

TL;DR

This paper provides a modern, comprehensive exposition of discrete series L-packets for real reductive groups, incorporating recent developments and new results to simplify understanding and proofs.

Contribution

It introduces recent advancements like normalized transfer factors and double covers, and proves new criteria for generic representations and explicit formulas for transfer factors.

Findings

Incorporates recent developments such as normalized transfer factors.

Provides a simple criterion for detecting generic representations.

Derives an explicit formula for the transfer factor elta_I in terms of covers of tori.

Abstract

We give a modern exposition of the construction, parameterization, and character relations for discrete series L-packets of real reductive groups, which are fundamental results due to Langlands and Shelstad. This exposition incorporates recent developments not present in the original sources, such as normalized geometric transfer factors and the canonical double covers of tori and endoscopic groups, allowing for simpler statements and proofs. We also prove some new results, such as a simple criterion for detecting generic representations for a prescribed Whittaker datum, and an explicit formula for the factor $\Delta_I$ in terms of covers of tori.