Irregular Hodge numbers of Frenkel--Gross connections

Frenkel and Gross constructed a family of connections on ${\mathbb{P}}^1\mathrm{\backslash }\{0,\mathrm{\infty }\}$, for almost simple groups $\check{G}$ and their representations. In this article, we calculate the irregular Hodge numbers of these Frenkel–Gross connections, and, as an application, we prove a conjecture of Katzarkov–Kontsevich–Pantev for mirror Landau-Ginzburg models of minuscule homogeneous spaces.