首页/论文/2004.08391

arXiv 2004.083912020-04-17math.RT

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

Nolan R. Wallach

备注：: arXiv admin note: substantial text overlap with arXiv:1902.01871

英文摘要：

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-Chandra modules developed in this paper plays a key role.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

任意特征下 Specht 模在逆 Schur 函子下的像

The image of the Specht module under the inverse Schur functor in arbitrary characteristic

本文研究了任意特征下 Specht 模在逆 Schur 函子下的像，给出了特征 2 下与对偶 Weyl 模同构的充要条件，并在其他特征下给出了初等证明，同时探讨了同构不成立时的商映射性质。

2023-09-11math.RT

降维与逆降维函子 I：标准 $\mathsf{V^k}(\mathfrak{sl}_2)$-模

Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules

Université Bourgogne Europe（勃艮第欧洲大学）；University of Melbourne（墨尔本大学）

本文研究了降维与逆降维函子的组合，重点探讨了标准 $\mathsf{V^k}(\mathfrak{sl}_2)$-模的性质，并通过最简单的例子计算了降维在关联于 $\mathfrak{sl}_2$ 的affine顶点算子代数的标准模上的作用。

2026-05-19math-phmath.MPmath.QA

An analog of the Deligne-Lusztig duality for $(\mathfrak{g},K)$-modules

Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor, on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We apply this to the category of (g,K)-modules, and we stipulate that the pseudo-identity functor is the analog of the Deligne-Lusztig functor. In order to support this, we show that the pseudo-identity functor for (g,K)-modules is isomorphic to the composition of cohomological and c…

2017-08-14math.RT

Notes on Restricted Inverse Limits of Categories

We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category of strict polynomial functors of finite degree, and it is the restricted inverse limit of the categories of polynomial representations of $GL_n$. This note is meant to serve as a reference for future work.

2015-04-05math.RT

On Categories of Admissible $\big(\mathfrak{g},\mathrm{sl}(2)\big)$-Modules

Let $\mathfrak{g}$ be a complex finite-dimensional semisimple Lie algebra and $\mathfrak{k}$ be any $\mathrm{sl}(2)$-subalgebra of $\mathfrak{g}$. In this paper we prove an earlier conjecture by Penkov and Zuckerman claiming that the first derived Zuckerman functor provides an equivalence between a truncation of a thick parabolic category $\mathcal{O}$ for $\mathfrak{g}$ and a truncation of the category of admissible $(\mathfrak{g}, \mathfrak{k})-$modules. This latter truncated category consists of admissible $(\mathfrak{g}, \mathfrak{k})-$modules with sufficiently large minimal $\mathfrak{k}$…

2016-04-16math.RT

Serre 函子与 $\mathbb{P}^n$ 上反常层的 $\mathbb{P}$-对象

Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$

本文证明了 $\mathbb{P}^n$ 上可构造导出范畴的逆 Serre 函子可由开层简单反常层的 $\mathbb{P}$-扭转实现，并证明所有不可分解反常层均为 $\mathbb{P}$-like 对象且显式构造了其自同态空间的生成态射。

2025-06-06math.AGmath.RT

更多相关论文收起更多论文

Koszul理论的表示论视角

A Representation theoretic perspective of Koszul theory

该研究从表示论视角建立Koszul理论新联系，通过组合描述局部Koszul复形与二次对偶，构造Koszul函子，得到新Koszul代数类、更强扩张猜想及导出范畴等价等结果。

2024-11-23math.RT

Duality and contravariant functors in the representation theory of artin algebras

We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ rather than of functors $R\textbf{-Mod}\to\textbf{Ab}$ which are given by a pp pair. This paper will give various algebraic characterisations of these functors in the case that $R$ is an artin algebra. Suppose that $R$ is an artin algebra. An additive functor $G:(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ preserves inverse limits and $G|_{(R\textbf{-mod})^{\text{op}}}:(R\textbf{-mod})^{\text{op}}\to\…

2017-02-23math.CTmath.LOmath.RT

Representation embeddings, interpretation functors and controlled wild algebras

We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of modules of finite-dimensional algebras induce embeddings of lattices of pp formulas and hence are non-decreasing on Krull-Gabriel dimension and uniserial dimension. A consequence is that the category of modules of any wild finite-dimensional algebra has width $\infty$ and hence, if the algebra is countable, there is a superdecomposable pure-injective representation. It is conjectured that a stronger result is true: t…

2015-07-02math.LOmath.RAmath.RT

On functors between module categories for associative algebras and for $\mathbb{N}$-graded vertex algebras

We prove that the weak associativity for modules for vertex algebras are equivalent to a residue formula for iterates of vertex operators, obtained using the weak associativity and the lower truncation property of vertex operators, together with a known formula expressing products of components of vertex operators as linear combinations of iterates of components of vertex operators. By requiring that these two formulas instead of the commutator formula hold, we construct a functor $S$ from the category of modules for Zhu's algebra of a vertex operator algebra $V$ to the category of $\mathbb{N}…

2013-10-22hep-thmath.QAmath.RT

Correspondences of categories for subregular W-algebras and principal W-superalgebras

Based on the Kazama-Suzuki type coset construction and its inverse coset between the subregular $\mathcal{W}$-algebras for $\mathfrak{sl}_n$ and the principal $\mathcal{W}$-superalgebras for $\mathfrak{sl}_{1|n}$, we prove weight-wise linear equivalences of their representation categories. Our main results are then improvements of these correspondences incorporating the monoidal structures. Firstly, in the rational case, we obtain the classification of simple modules and their fusion rules via simple current extensions from their Heisenberg cosets. Secondly, beyond the rational case, we use ce…

2021-04-02math-phmath.MPmath.QA