Semisimple Types in GLn
Semisimple Types in GLn
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GLn 中的半简单类型
DOI：
10.1023/a:1001773929735
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发表时间：
1999
影响因子：
1.8
通讯作者：
P. Kutzko
中科院分区：
文献类型：
--
作者：
C. Bushnell;P. Kutzko
本文研究非阿基米德局部域F的一般线性群G=GL(F)的光滑表示理论，重点是紧开子群的一系列特殊的不可约表示的(显式)构造，称为半单型，以及它们的Hecke代数的计算.给定的半单型决定了G的光滑表示范畴的Bernstein分支；该分支是仿射Hecke代数的张量积的模范畴；每个分支都是这样产生的。此外，利用仿射Hecke代数之间的标准映射刻画了连接G及其Levi子群的所有Jacquet函子和抛物诱导函子。半单型的这些性质依赖于其特殊的交织性质，而这些性质又隐含着系数函数的支撑性的强界。
This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of irreducible representations of compact open subgroups, called semisimple types, and the computation of their Hecke algebras. A given semisimple type determines a Bernstein component of the category of smooth representations of G; that component is then the module category for a tensor product of affine Hecke algebras; every component arises this way. Moreover, all Jacquet functors and parabolic induction functors connecting G with its Levi subgroups are described in terms of standard maps between affine Hecke algebras. These properties of semisimple types depend on their special intertwining properties which in turn imply strong bounds on the support of coefficient functions.