Bushnell, Colin J.; Henniart, Guy
The Local Langlands Conjecture for GL(2)
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 t
he structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.
- Verlag: Springer, Berlin
- Ausstattung: 2006. 350 p.
- ISBN: 3540314865
- Preis: 81,95 €
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