Generators of a Picard modular group in two complex dimensions

TL;DR

This paper proves that four specific transformations generate the Picard modular group over Gaussian integers in two complex dimensions, confirming a previously posed question.

Contribution

It explicitly identifies generators for the two-dimensional Picard modular group over Gaussian integers, resolving an open question.

Findings

Four transformations generate the group

The result confirms a conjecture by Kleinschmidt and Persson

Provides explicit generators for the group

Abstract

The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space. The result answers positively a question raised by A. Kleinschmidt and D. Persson.