Classification of Rigid Irregular $G_2$-Connections

Abstract

Using the Katz-Arinkin algorithm we give a classification of irreducible rigid irregular connections on a punctured ${\mathbb{P}}_{\mathbb{C}}^1$ having differential Galois group $G_2$, the exceptional simple algebraic group, and slopes having numerator 1. In addition to hypergeometric systems and their Kummer pull-backs we construct families of $G_2$-connections which are not of these types.

Cited by in corpus (3)

• Euphotic representations and rigid automorphic data
• Wildly Ramified Rigid $G_2$-Local Systems
• Irregular Hodge numbers for rigid $G_2$-connections