关于Braverman-Kazhdan的猜想

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2021-12-02 DOI:10.1090/jams/992

Tsao-Hsien Chen

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引用次数: 0

摘要

摘要:本文证明了Braverman-Kazhdan的一个猜想。功能。分析的。[专题卷(2000)，pp. 237-278]关于$\rho$-贝塞尔轴在还原基上的不周期性。我们通过证明在我们之前的工作中提出的一个消失猜想来做到这一点[a消失猜想:GLn情况，arXiv:1902.11190]。作为推论，我们得到了由Braverman和Kazhdan猜想的有限约化群的非线性傅里叶核的几何构造。利用Mellin变换理论、Harish-Chandra双模的Drinfeld中心以及混合特征中一类特征束的构造进行了证明。

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On a conjecture of Braverman-Kazhdan

Abstract:In this article we prove a conjecture of Braverman-Kazhdan in [Geom. Funct. Anal. Special Volume (2000), pp. 237–278] on acyclicity of $\rho$-Bessel sheaves on reductive groups. We do so by proving a vanishing conjecture proposed in our previous work [A vanishing conjecture: the GLn case, arXiv:1902.11190]. As a corollary, we obtain a geometric construction of the non-linear Fourier kernel for a finite reductive group as conjectured by Braverman and Kazhdan. The proof uses the theory of Mellin transforms, Drinfeld center of Harish-Chandra bimodules, and a construction of a class of character sheaves in mixed-characteristic.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.