Irregular Hodge numbers of Frenkel--Gross connections

TL;DR

This paper computes the irregular Hodge numbers of Frenkel--Gross connections and proves a related mirror symmetry conjecture for Landau-Ginzburg models of minuscule homogeneous spaces.

Contribution

It provides explicit calculations of irregular Hodge numbers for a family of connections and confirms a conjecture linking these to mirror symmetry in algebraic geometry.

Findings

Calculated irregular Hodge numbers for Frenkel--Gross connections

Proved a conjecture of Katzarkov--Kontsevich--Pantev for mirror Landau-Ginzburg models

Established connections between irregular Hodge theory and mirror symmetry

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.