Description
Book SynopsisThe Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and 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.
Trade ReviewFrom the reviews:
"In this book the authors present a complete proof of the Langlands conjecture for GL (2) over a non-archimedean local field, which uses local methods and is accessible to students. … The book is very well written and easy to read." (J. G. M. Mars, Zentralblatt MATH, Vol. 1100 (2), 2007)
"The book under review gives a complete and self-contained insight into the theory of representations of G. … We highly recommend this book to Ph.D. students as well as to specialists. The book contains a huge amount of information, definition and facts … . The book has a Bibliography containing 91 references … ." (Alexandru Ioan Badulescu, Mathematical Reviews, Issue 2007 m)
“The aim of this monograph is to present a complete and self-contained proof of the Langlands conjecture for GL(2) over a non-archimedean local field. … This volume presents a large amount of difficult material in a clear and readable manner. It can be recommended to anyone interested in representations of linear algebraic groups.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)
Table of ContentsSmooth Representations.- Finite Fields.- Induced Representations of Linear Groups.- Cuspidal Representations.- Parametrization of Tame Cuspidals.- Functional Equation.- Representations of Weil Groups.- The Langlands Correspondence.- The Weil Representation.- Arithmetic of Dyadic Fields.- Ordinary Representations.- The Dyadic Langlands Correspondence.- The Jacquet-Langlands Correspondence.
