Generators of Eisenstein--Picard modular group in three complex dimensions

Abstract

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein--Picard modular group $\mathbf{PU}(3,1;\mathbb{Z}[{\omega }_3])$ in three complex dimensions can be generated by four given transformations.

8 pages