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arXiv · 1609.03292

Classification of Rigid Irregular $G_2$-Connections

Konstantin Jakob
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Abstract

Using the Katz-Arinkin algorithm we give a classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ 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.

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BibTeXRIS

Konstantin Jakob. 2016-09-12. Classification of Rigid Irregular $G_2$-Connections. https://doi.org/10.1112/plms.12308

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