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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中文翻译：

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关于 Braverman-Kazhdan 的猜想

摘要：在本文中，我们证明了 [Geom. 功能。肛门。Special Volume (2000), pp. 237–278] 关于还原群上 $\rho$-Bessel 滑轮的非循环性。我们通过证明我们之前工作中提出的消失猜想来做到这一点[消失猜想：GLn 案例，arXiv:1902.11190]。作为推论，我们得到了 Braverman 和 Kazhdan 猜想的有限约简群的非线性傅里叶核的几何构造。证明使用了 Mellin 变换理论、Harish-Chandra 双模的 Drinfeld 中心和混合特征中的一类特征层的构造。

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