On the physical rigidity of Frenkel-Gross connection

We show that the Frenkel-Gross connection on \({\mathbb {G}}_m\) ${\mathbb{G}}_m$ is physically rigid as \(\check{G}\) $\check{G}$ -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 \(\check{G}\) $\check{G}$ -connection with only generic oper structure, using the localization of Weyl modules.