Overview
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 groupsand the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.
Full Product Details
Author: Colin J. Bushnell ,
Guy Henniart
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: Softcover reprint of hardcover 1st ed. 2006
Volume: 335
Dimensions:
Width: 15.50cm
, Height: 1.90cm
, Length: 23.50cm
Weight: 0.557kg
ISBN: 9783642068539
ISBN 10: 3642068537
Pages: 340
Publication Date: 23 November 2010
Audience:
Professional and scholarly
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: Out of print, replaced by POD
We will order this item for you from a manufatured on demand supplier.
Reviews
From 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)
From 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)
