Irregular Hodge numbers of Frenkel--Gross connections

Abstract

Frenkel and Gross constructed a family of connections on ${\mathbb{P}}^1\backslash \{0,\infty \}$, 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.