Hypergeometric sheaves with tannakian monodromy group $G_2$

TL;DR

This paper proves that a specific hypergeometric sum has a Tannakian monodromy group of type G_2, using Katz's Fourier transform uniformity results to establish the monodromy group explicitly.

Contribution

It identifies the monodromy group of a hypergeometric sum as G_2, providing a new example of such monodromy groups in the context of hypergeometric sheaves.

Findings

Monodromy group of the hypergeometric sum is G_2

Application of Katz's Fourier transform results to determine monodromy

Explicit identification of the Tannakian monodromy group

Abstract

Based on a suggestion by Katz, we determine the monodromy group of a certain hypergeometric sum to be $G_2$. Our approach is based on the uniformity results by Katz on the Fourier transform to deduce uniformity for the Tannakian monodromy groups.