A formula for the geometric Jacquet functor and its character sheaf analogue
A formula for the geometric Jacquet functor and its character sheaf analogue
复制标题
几何 Jacquet 函子的公式及其特征束类似物
DOI：
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发表时间：
2015
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通讯作者：
Alexander Yom Din
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文献类型：
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作者：
Tsao;Alexander Yom Din
设(G，K)是复数上的对称对，$${X=K反斜杠G}$$X=KG是对应的对称空间。在这篇文章中，我们研究了与X退化到$${MN反斜杠G}$$MNG有关的附近的循环函子，我们称之为“奇妙退化”。我们证明了在X上的特征标轮范畴上，这个函子同构于两个平均函子的合成(在p-进设置下的函数水平上，在[BK，Sv]中得到了类似的结果)。作为应用，我们得到了[ENV]的几何Jacquet函子的一个公式，并利用这个公式给出了著名的Casselman子模定理的几何证明，并建立了Harish-Chandra模的第二个伴随定理。
Let (G,K) be a symmetric pair over the complex numbers, and let $${X=K ackslash G}$$X=KG be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to $${MN ackslash G}$$MNG, which we call the “wonderful degeneration”. We show that on the category of character sheaves on X, this functor is isomorphic to a composition of two averaging functors (a parallel result, on the level of functions in the p-adic setting, was obtained in [BK,SV]). As an application, we obtain a formula for the geometric Jacquet functor of [ENV] and use this formula to give a geometric proof of the celebrated Casselman’s submodule theorem and establish a second adjointness theorem for Harish-Chandra modules.