D-modules on the basic affine space and large g-modules

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-17 DOI:10.1016/j.jalgebra.2025.06.037

Masatoshi Kitagawa

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引用次数: 0

Abstract

In this paper, we consider

D

-modules on the basic affine space

G / U

and their global sections for a semisimple complex algebraic group G. Our aim is to prepare basic results about large non-irreducible modules for the branching problem and harmonic analysis of reductive Lie groups. A main tool is a formula given by Bezrukavnikov–Braverman–Positselskii. The formula is about a product of functions and their Fourier transforms on

G / U

like Capelli's identity. Using the formula, we give a generalization of the Beilinson–Bernstein correspondence.

It is also shown that the global sections of holonomic

D

-modules are also holonomic using the formula. As a consequence, we give a large algebra action on the

u

-cohomologies

H^{i} (u; V)

of a

g

-module V when V is realized as a holonomic

D

-module. We consider affinity of the supports of the

t

-modules

H^{i} (u; V)

查看原文本刊更多论文

基本仿射空间上的d模和大g模

本文考虑了半简单复代数群G的基本仿射空间G/U上的d模及其整体截面，目的是为可约李群的分支问题和调和分析提供关于大不可约模的基本结果。一个主要的工具是Bezrukavnikov-Braverman-Positselskii给出的公式。这个公式是关于函数和它们在G/U上的傅里叶变换的乘积就像Capelli恒等式一样。利用该公式，我们给出了贝林森-伯恩斯坦对应的推广。利用公式还证明了完整d模的整体截面也是完整的。因此，当g模V被实现为完整的d模时，我们给出了对g模V的u-上同调Hi（u；V）的一个大代数作用。我们考虑了t模Hi（u；V）支承的亲和性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.