Thinness of some hypergeometric groups in Sp(6)

TL;DR

This paper proves that certain hypergeometric groups associated with specific parameter pairs are thin, contributing to the understanding of their algebraic and geometric properties within the symplectic group Sp(6).

Contribution

It demonstrates the thinness of hypergeometric groups for seven specific parameter pairs, a novel result in the study of these groups.

Findings

Seven hypergeometric groups are thin.

The groups correspond to specific parameter pairs.

This advances knowledge of hypergeometric group structures.

Abstract

We show that the hypergeometric groups corresponding to the seven pairs of the parameters $\alpha$, $\beta$ where $\alpha$ = (0, 0, 0, 0, 0, 0) and $\beta$ is any of the parameters (1/2, 1/2, 1/2, 1/2, 1/2, 1/2), (1/2, 1/2, 1/2, 1/2, 1/3, 2/3), (1/2, 1/2, 1/2, 1/2, 1/4, 3/4), (1/2, 1/2, 1/2, 1/2, 1/6, 5/6), (1/2, 1/2, 1/3, 2/3, 1/3, 2/3), (1/2, 1/2, 1/3, 2/3, 1/4, 3/4), (1/2, 1/2, 1/5, 2/5, 3/5, 4/5) are thin.