The Local Langlands Conjecture for GL(2)

  • Colin J. Bushnell
  • Guy Henniart

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 335)

Table of contents

About this book

Introduction

If F is a non-Archimedean local field, local class field theory can be viewed as giving a canonical bijection between the characters of the multiplicative group GL(1,F) of F and the characters of the Weil group of F. If n is a positive integer, the n-dimensional analogue of a character of the multiplicative group of F is an irreducible smooth representation of the general linear group GL(n,F). The local Langlands Conjecture for GL(n) postulates the existence of a canonical bijection between such objects and n-dimensional representations of the Weil group, generalizing class field theory.

This conjecture has now been proved for all F and n, but the arguments are long and rely on many deep ideas and techniques. This book gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.

Keywords

Local Langlands correspondence Representation theory Weil group finite field functional equation smooth representation

Authors and affiliations

  • Colin J. Bushnell
    • 1
  • Guy Henniart
    • 2
  1. 1.Department of MathematicsKing's College LondonWC2R 2LSStrandUK
  2. 2.Département de MathématiquesUniversitéde Paris-Sud et umr 8628 du CNRS91405France

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-31511-X
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-31486-8
  • Online ISBN 978-3-540-31511-7
  • Series Print ISSN 0072-7830
  • About this book