The Langlands spectral decomposition

TL;DR

This paper surveys the Langlands spectral decomposition theorem, focusing on the meromorphic continuation of Eisenstein series and the role of intertwining operators in their functional equations.

Contribution

It provides an overview of the spectral decomposition theorem within the Langlands program, emphasizing the analytic continuation and functional equations of Eisenstein series.

Findings

Highlights the importance of meromorphic continuation of Eisenstein series.

Explains the role of intertwining operators in spectral decomposition.

Summarizes key aspects of the Langlands spectral decomposition theorem.

Abstract

This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published by Cambridge University Press. This is a survey of Langlands spectral decomposition theorem based on the meromorphic continuation of Eisenstein series and intertwining operators that show up in their functional equations.