The Local Langlands Conjecture for Gl(2)
The Local Langlands Conjecture for Gl(2)
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DOI：
10.1007/3-540-31511-x
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
C. Bushnell;G. Henniart
中科院分区：
文献类型：
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作者：
C. Bushnell;G. Henniart
若F是非阿基米德局部域，则局部类域理论可以看作给出F的乘法群GL（1，F）的特征标与F的Weil群的特征标之间的一个典范双射。如果n是正整数，则F的乘法群的特征标的n维模拟是一般线性群GL（n，F）的不可约光滑表示。GL（n）的局部朗兰兹猜想假设在这样的对象和Weil群的n维表示之间存在一个规范的双射，推广了类场论。这个猜想现在已经证明了所有的F和n，但论点很长，并依赖于许多深刻的想法和技术。这本书给出了一个完整的和自足的证明朗兰兹猜想的情况下n= 2。它的对象是研究生和相关领域的研究人员。它的先决条件没有特殊的知识以外的开端表示理论的有限群和结构理论的地方领域。它只使用局部的方法，对adele群上的调和分析没有吸引力。
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 the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.