On the physically rigidity of Frenkel-Gross connection

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.