On the physical rigidity of Frenkel-Gross connection

Selecta Mathematica Pub Date : 2024-04-03 DOI:10.1007/s00029-024-00931-9

Lingfei Yi

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Abstract

We show that the Frenkel-Gross connection on ${\mathbb {G}}_m$ is physically rigid as $\check{G}$-connection, thus confirming the de Rham version of a conjecture of Heinloth-Ngô-Yun. The proof is based on the construction of the Hecke eigensheaf of a $\check{G}$-connection with only generic oper structure, using the localization of Weyl modules.

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论 Frenkel-Gross 连接的物理刚性

我们证明了关于 ${\mathbb {G}}_m$ 的 Frenkel-Gross 连接作为 $\check{G}$ 连接在物理上是刚性的，从而证实了 Heinloth-Ngô-Yun 猜想的 de Rham 版本。这个证明基于利用韦尔模块的局部化构造一个只有泛型 oper 结构的 $\check{G}$-connection 的 Hecke eigensheaf。

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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