Generators for the Euclidean Picard Modular Groups

Abstract

The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain the relations of the isotropy subgroup by analysis of the combinatorics of the fundamental domain in Heisenberg group.

25 pages,12 figures

References in corpus (2)

• Complex hyperbolic triangle groups
• An explicit fundamental domain for the Picard modular group in two complex dimensions