The Local Langlands Conjecture for GL(2) - Colin J. Bushnell, Guy Henniart

The Local Langlands Conjecture for GL(2)

Buch | Softcover
XII, 340 Seiten
2010 | 1. Softcover reprint of hardcover 1st ed. 2006
Springer Berlin (Verlag)
978-3-642-06853-9 (ISBN)
171,19 inkl. MwSt

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.

Smooth 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.

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)“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)

Erscheint lt. Verlag 23.11.2010
Reihe/Serie Grundlehren der mathematischen Wissenschaften
Zusatzinfo XII, 351 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 550 g
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte finite field • functional equation • Local Langlands correspondence • Representation Theory • smooth representation • Weil group
ISBN-10 3-642-06853-7 / 3642068537
ISBN-13 978-3-642-06853-9 / 9783642068539
Zustand Neuware
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