On the physically rigidity of Frenkel-Gross connection

TL;DR

This paper proves the physical rigidity of the Frenkel-Gross connection, confirming a conjecture and advancing understanding of its geometric and algebraic properties.

Contribution

It establishes the physical rigidity of the Frenkel-Gross connection and confirms the de Rham version of a conjecture by Heinloth-Ngô-Yun.

Findings

Frenkel-Gross connection is physically rigid as a -connection.

Constructs the Hecke eigensheaf for a connection with generic oper structure.

Uses localization of Weyl modules in the proof.

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-Ng\^o-Yun. The proof is based on the construction of the Hecke eigensheaf of a connection with only generic oper structure, using the localization of Weyl modules.