On the physically rigidity of Frenkel-Gross connection

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 connection with only generic oper structure, using the localization of Weyl modules.

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