The Local Langlands Conjecture for GL(2)

• Main Authors: Bushnell, Colin J. (Author), Henniart, Guy (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 335
• Subjects: Mathematics.; Group theory.; Topological groups.; Lie groups.; Number theory.; Number Theory.; Topological Groups, Lie Groups.; Group Theory and Generalizations.

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 multip...

Table of Contents:

• 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.