Math

Letter to Godement

Author: 
Robert P. Langlands
Year: 
1967
Type: 
article

Editorial comments: The letter to Weil that saw the birth of the L-group was written in January 1967. Somewhat later that same year, Roger Godement asked Langlands to comment on the Ph.D. thesis of Hervé Jacquet. His reply included a number of conjectures on Whittaker functions for both real and p-adic reductive groups. These were later to be proven, first in the p-adic case by Shintani for GLn and Casselman Shalika in general, and much later in the real case by a longer succession of people.

School of Mathematics: 

Problems in the Theory of Automorphic Forms

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Lectures in modern analysis and applications III, Lecture Notes in Mathematics

Volume: 
170
Year: 
1970
Type: 
article
Keywords: 
Functoriality
MathReview: 
302614

Editorial comments: The conjectures made in the 1967 letter to Weil were explained here more fully. This appeared originally as a Yale University preprint, later in the published proceedings of a conference in Washington, D.C. Lectures in modern analysis and applications III, Lecture Notes in Mathematics 170, Springer-Verlag, 1970. The lecture is dedicated to Salomon Bochner. 

School of Mathematics: 

Dimension of spaces of automorphic forms

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Proceedings of the AMS Symposium at Boulder, Colorado

Year: 
1965
Type: 
article
MathReview: 
212135

Author's comments: Although the principal purpose of this paper was to review how the Selberg trace formula is combined with character formulas to calculate the dimension of various spaces of automorphic forms, it is included as a paper on representation theory because the most influential observation in the paper was the description of a possible realization of the discrete series representations on spaces of L2-cohomology.

School of Mathematics: 

On unitary representations of the Virasoro algebra

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Infinite-dimensional Lie algebras and their applications

Year: 
1988
Publisher: 
World Scientific
Type: 
article
MathReview: 
1114998

Author's comments: This paper, or some aspects of this paper, have been called into question in

https://mathoverflow.net/q/144419.

School of Mathematics: 

Euler Products

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Yale Mathematical Monographs

Year: 
1967
Type: 
article
Keywords: 
Eisenstein
MathReview: 
419366

Euler Products Cover Page

Editorial comments: The letter to Weil included a number of striking conjectures which eventually changed much of the direction of research in automorphic forms. Some of their consequences were explained in a graduate course given at Princeton in the spring of 1967, and then things were put in a somewhat wider context in a series of lectures at Yale later that Spring. These notes were previously published as the first of the Yale Mathematical Monographs.

School of Mathematics: 

Notes on the Knapp-Zuckerman theory

Author: 
Robert P. Langlands
Last Name: 
Journal
Journal: 

Unpublished

Year: 
1977
Type: 
article

Editorial comments: This has not been published before. It was written around 1977, just after A. Knapp and G. Zuckerman had announced their results on reducible unitary principal series, subsequently explained in a talk at the A.M.S. 1977 summer school in Corvallis (pp. 93--105 of the published proceedings of that conference.)

School of Mathematics: 

Letter to André Weil

Author: 
Robert Langlands
Last Name: 
Langlands
Journal
Journal: 

Emil Artin and beyond---Class field theory and L-functions

Year: 
written in 1967, appeared in volume in 2015
Pages: 
165--173
Publisher: 
European Mathematical Society
Type: 
article
Keywords: 
Functoriality

Editorial comments: In January of 1967, while he was at Princeton University, Langlands wrote a letter of 17 hand-written pages to Andre Weil outlining what quickly became known as `the Langlands conjectures'. This letter even today is worth reading carefully, although its notation is by present standards somewhat clumsy. It was in this letter that what later became known as the `L-group' first made its appearance, like Gargantua, surprisingly mature.

School of Mathematics: 

Pages