Jacquet modules of locally analytic representations of p-adic reductive groups -: I.: Construction and first properties
Jacquet modules of locally analytic representations of p-adic reductive groups -: I.: Construction and first properties
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DOI：
10.1016/j.ansens.2006.08.001
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发表时间：
2006-09-01
影响因子：
1.9
通讯作者：
Emerton, Matthew
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文献类型：
--
作者：
Emerton, Matthew
令G为在P-ADIC局部场L上定义的还原组，让P为Levi商M的G抛物线子组，并写入G：= G（L），P：= P（L）和M： = m（l）。在本文中，我们从本质上可接受的本地分析g代表类别构建了一个函子j（p），从本质上可以接受的本地分析M代表性类别中，我们称之为jacquet模块函数，该模块与p相关，以及与P的重合相关的jacquet模块。 [Casselman W.的常规Jacquet模块函数，P-Adic还原群体可接受代表理论的简介， P. Sally发表的未发表的注释，日期为1993年5月7日草案。可通过http://www.math.ubc.ca/people/faculty/faculty/cass/research.html获得电子方式。 [5]]在可允许的平滑g代表的子类别上。我们建立了该函子的几个重要属性。 （c）2006年由Elsevier Masson SAS出版。
Let G be a reductive group defined over a p-adic local field L, let P be a parabolic subgroup of G with Levi quotient M, and write G := G(L), P := P(L), and M := M(L). In this paper we construct a functor J(P) from the category of essentially admissible locally analytic G-representations to the category of essentially admissible locally analytic M-representations, which we call the Jacquet module functor attached to P, and which coincides with the usual Jacquet module functor of [Casselman W., Introduction to the theory of admissible representations of p-adic reductive groups, unpublished notes distributed by P. Sally, draft dated May 7, 1993. Available electronically at http://www.math.ubc.ca/people/faculty/cass/research.html. [5]] on the subcategory of admissible smooth G-representations. We establish several important properties of this functor. (c) 2006 Published by Elsevier Masson SAS.