REPRESENTATIONS OF THE GROUP GL(n, F) WHERE F IS A NON-ARCHIMEDEAN LOCAL FIELD
REPRESENTATIONS OF THE GROUP GL(n, F) WHERE F IS A NON-ARCHIMEDEAN LOCAL FIELD
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DOI：
10.1070/rm1976v031n03abeh001532
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发表时间：
1976-06
影响因子：
0.9
通讯作者：
I. N. Bernshtein;A. V. Zelevinskii
中科院分区：
文献类型：
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作者：
I. N. Bernshtein;A. V. Zelevinskii
本文综述了约化群表示理论的最新结果。为简单起见，仅处理群GL(N)。第一章提供了关于局部紧零维群表示的一般信息。第二章介绍了Harish-Chandra研究GL(N)的表示的方法，该方法基于对尖点表示的约化。用这种方法证明了一些有限定理。在第三章中，我们研究了Gel‘fand和Kazhdan给出的GL(N)表示的另一种方法，它是基于将GL(N)的表示限制在一个子群Pn上。所有的定理都有详细的证明。读者除了对非阿基米德局部场的结构有最基本的熟悉外，不假定有任何先验信息。
This article is a survey of recent results in the theory of representations of reductive -adic groups. For simplicity of presentation only the groups GL(n) are treated. Chapter I provides general information on representations of locally compact zero-dimensional groups. Chapter II presents Harish-Chandra's method of studying the representations of GL(n), which is based on reduction to cuspidal representations. Some finiteness theorems are proved by this method. In Chapter III we study another approach to the representations of GL(n), due to Gel'fand and Kazhdan; it is based on restricting the representations from GL(n) to a subgroup Pn. All theorems are presented with detailed proofs. No prior information is assumed on the part of the reader except the most elementary familiarity with the structure of non-Archimedean local fields.