Pure elements and intertwining classes of simple strata in local central simple algebras
Pure elements and intertwining classes of simple strata in local central simple algebras
复制标题
局部中心简单代数中简单层的纯元素和交织类
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Martin Grabitz
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文献类型：
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作者：
P. Broussous;Martin Grabitz
设G = GL，（D）是以padic域F为中心的除代数D上的一般线性群。证明了G的光滑对偶可以象Bushnell和Kutzko对G L N（F）所做的那样构造[BK 2].验证这样一个猜想意味着大量的运算、推理和计算。本文的目的是建立关于简单层的一些基本结果：“交织~g蕴涵共轭”性质和与纯层等价的简单层的存在性。这实际上使我们能够定义超尖点表示的简单类型。
Let G = GL,,,(D) be the general linear group over a division algebra D with centre a padic field F. It has been conjectured that the smooth dual of G can be constructed as Bushnell and Kutzko did for G L N ( F ) [BK2]. Checking such a conjecture means a lot of const,rurtions and computations. The aim of this paper is to establish some fundamental results on simple strata: the "intertwini~~g implies conjugacy" property and the existence of a simple stratum equivalent to a pure one. This virtually enables us to define simple types for supercuspidal representations.