Twisted homology for the mirabolic nilradical
Twisted homology for the mirabolic nilradical
复制标题
mirabolic nilradical 的扭曲同源性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Sahi
中科院分区：
文献类型：
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作者：
Avraham Aizenbud;D. Gourevitch;S. Sahi
在[BZ77]中定义了GL（n，n，p）的光滑表示的导数的概念。在阿基米德的情况下，最高导数的类似物在[Sah 89]中被定义为不可约酉表示，并被称为“引”表示。在[AGS]中，所有阶导数都被定义为光滑容许Fréchet表示（中等增长）。这个定义的一个关键成分是关于Mirabolic子群的零根的扭曲共不变量的函子。本文证明了这一函子的正合性，并计算了它在一类表示上的正合性。这意味着最高导函子的正合性，并允许计算所有单项式表示的最高导.在[AGS]中，这些结果被应用于完成所有不可约酉表示的导出表示的计算，并证明了酉表示的退化Whittaker模型的唯一性.
The notion of derivatives for smooth representations of GL(n, ℚp) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In [AGS] derivatives of all orders were defined for smooth admissible Fréchet representations (of moderate growth).A key ingredient of this definition is the functor of twisted coinvariants with respect to the nilradical of the mirabolic subgroup. In this paper we prove exactness of this functor and compute it on a certain class of representations. This implies exactness of the highest derivative functor, and allows to compute highest derivatives of all monomial representations.In [AGS] these results are applied to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations.