On the Casselman-Jacquet functor

无多重性Jacquet模

Multiplicity free Jacquet modules

设F是非阿基米德局部域或有限域。设n为自然数，k为1或2。考虑G：=GL（n+k，F），设M：=GL（n，F）× GL（k，F）<G是极大Levi子群.设U< G是相应的幂幺子群，P=MU是相应的抛物子群.设J表示从G的表示到M的表示的Jacquet函子（即关于G的共不变式的函子）。U）。本文证明了对G的任何不可约表示π和M的任何ρ，J是一个无重函子，即dim Hom（J（π），ρ）<= 1.要做到这一点，我们适应的经典方法Gelfand和Kazhdan证明“多重性自由”性质的某些表示证明“多重性自由”性质的某些函子。最后讨论了其它Jacquet函子是否是多重自由的。

Jacquet函子与De Concini-Procesi紧化

Jacquet functor and De Concini-Procesi compactification

我们使用De Concini-Procesi紧化的变形给出Jacquet函子的几何实现。

抛物归纳的广义Jacquet模

Generalized Jacquet modules of parabolic induction

本文研究了抛物归纳法的Jacquet模的一个推广，并在其上构造了一个滤子，利用扭函子写出了滤子的连商。

An adjunction formula for the Emerton-Jacquet functor

The Emerton-Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here we give an adjunction formula for the Emerton-Jacquet functor, relating it directly to locally analytic inductions, under a strict hypothesis that we call non-critical. We also further study the relationship to socles of principal series in the non-critical setting.

Towards the Derived Jacquet-Emerton Module Functor

Let $G$ be a $p$-adic Lie group associated to a connected reductive group over $\mathbb{Q}_{p}$. Let $P$ be a parabolic subgroup of $G$ and let $M$ be a Levi quotient of $P$. In this paper, we define a $δ$-functor $H^{\star}J_{P}$ from the category of admissible locally analytic $G$-representations to the category of essentially admissible locally analytic $M$-representations that extends the Jacquet-Emerton module functor $J_{P}$ defined by Emerton.

非Borel抛物子群的Emerton Jacquet函子

Emerton's Jacquet functors for non-Borel parabolic subgroups

本文研究了p-adic约化群的局部解析表示的Emerton的Jacquet模函子。当P是一个抛物子群，其Levi因子M不是可交换的时，我们证明了传递到M的导出子群的同构子空间会产生环面Z（M）的本质容许的局部解析表示，这在刚性几何中有一个自然的解释.我们用它来扩展埃默顿的代表性理论建设的本征品种，通过构建本征品种内插自守表示，其本地组件在p不一定是主列。

仿射Jacquet函子与Harish-Chandra范畴

Affine Jacquet functors and Harish-Chandra categories

本文定义了仿射Jacquet函子，并用它来描述非临界水平上诱导仿射Harish-Chandra模的结构，推广了Kac和Kazhdan [KK]关于Bernstein-Gelfand-Gelfand范畴O中韦尔马模结构的定理.这是结合消失的结果，某些扩张群，以构建块分解的仿射Harish-Chandra模的类别连和Zuckerman [LZ]。后者是Rocha-Caridi，Wallach [RW]和Deodhar，Gabber，Kac [DGK]关于Kac-Moody代数的BGG范畴的块分解的工作的推广.我们还证明了仿射Jacquet函子与Kazhdan-Lusztig张量积之间的相容关系。本文利用这一结果证明了仿射Harish-Chandra范畴在与Kazhdan-Lusztig范畴的融合张量下是稳定的（我们的有限性结果[Y]的一个例子），并进一步应用于基于融合张量积的Kac-Moody代数平移函子的研究.

p-adic局部解析表示的Jacquet-Langlands函子

A Jacquet-Langlands functor for $p$-adic locally analytic representations

本文研究了无限层局部Shimura品种的局部解析理论，证明了不同周期sheaves在无限层的局部解析向量与p-adic李群作用无关，并展示了Jacquet-Langlands函子与局部解析向量及李代数中心字符的兼容性。

The dependence on parameters of the inverse functor to the $K$-finite functor

An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fréchet modules of moderate growth to the category of Harish-Chandra modules for a real reductive group, $G$ (here $K$ is a maximal compact subgroup of G).In this paper we study the dependence of this functor on parameters. Our main result implies that holomorphic dependence implies holomorphic dependence. The work uses results from the excellent thesis of van der Noort. Also a remarkable family of Universal Harish-Ch…

一般线性群上翻译函子与雅凯函子的比较

Comparing Translation and Jaquet functor over general linear groups

本文基于Chan和Wong构造的GL(n,ℂ)哈里什-钱德拉模块到A型分次赫克代数模块的函子，证明其关联了实侧翻译函子与p-adic侧雅凯函子。

$p$-adic sheaves on classifying stacks, and the $p$-adic Jacquet-Langlands correspondence

We establish several new properties of the $p$-adic Jacquet-Langlands functor defined by Scholze in terms of the cohomology of the Lubin-Tate tower. In particular, we reprove Scholze's basic finiteness theorems, prove a duality theorem, and show a kind of partial Künneth formula. Using these results, we deduce bounds on Gelfand-Kirillov dimension, together with some new vanishing and nonvanishing results. Our key new tool is the six functor formalism with solid almost $\mathcal{O}^+/p$-coefficients developed recently by the second author [Man22]. One major point of this paper is to extend the …

约化p-adic群的第二伴随定理

The Second Adjointness Theorem for reductive p-adic groups

在R-模上光滑群表示的一般性下，证明了非阿基米德局部域上约化群的抛物子群的Jacquet限制函子与其相反的抛物子群的抛物归纳函子是右伴随的，其中R的剩余域特征是可逆的.更正：原来这篇论文包含一个错误（在引理3.4中），作者一直无法修复。这使得主要定理的证明不完整。

与极大抛物子群相关的扭Jacquet模及$GL(n, q)$的尖表示

Twisted Jacquet modules associated to maximal parabolic subgroups and cuspidal representations of $GL(n, q)$

本文研究有限域上一般线性群尖表示关于极大抛物子群的扭Jacquet模的结构，通过建立扭Jacquet函子的范畴等价并构造具有泛性质的表示，直接解决了所有参数情形下的模结构问题。

约化李代数的可区分模的湮没簇

Annihilator varieties of distinguished modules of reductive Lie algebras

本文研究实约化群可区分表示的微局域必要条件，推广Vogan定理，应用于分支问题、混合模型及局部theta对应，并验证Prasad猜想。